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Takeaki Yamazaki

Faculty
Department of Electrical and Electronic Engineering
Course of Electricity, Electronics and Communications
PositionProfessor
Mail
HomepageURL
Birthday
Last Updated :2020/07/09

Researcher Profile and Settings

Education

  • Tokyo University of Science, Graduate School of Science

Academic & Professional Experience

  •   2016 04  - 現在, Toyo University, Faculty of Science and Engineering
  •   2011 04  - 2016 03 , Toyo University, Faculty of Science and Engineering
  •   2006  - 2007 , Kanagawa University, Faculty of Engineering
  •   2004  - 2006 , Kanagawa University, Faculty of Engineering
  •   2000  - 2004 , Kanagawa University, Faculty of Engineering

Research Activities

Research Areas

  • Natural sciences, Basic analysis

Research Interests

    Operator Theory

Published Papers

  • The Ando-Hiai inequalities for the solution of the generalized Karcher equation and related results, YAMAZAKI TAKEAKI, Journal of Mathematical Analysis and Applications, Journal of Mathematical Analysis and Applications, 479, (1) 531 - 545, 11 , Refereed
  • UPPER AND LOWER BOUNDS, AND OPERATOR MONOTONICITY OF AN EXTENSION OF THE PETZ-HASEGAWA FUNCTION, Takayuki Furuta, Masatoshi Ito, Takeaki Yamazaki, Masahiro Yanagida, MATHEMATICAL INEQUALITIES & APPLICATIONS, MATHEMATICAL INEQUALITIES & APPLICATIONS, 21, (1) 155 - 164, 01 , Refereed
  • Some properties of weighted operator means and characterizations of interpolational means, Yoichi Udagawa, Takeaki Yamazaki, Masahiro Yanagida, LINEAR ALGEBRA AND ITS APPLICATIONS, LINEAR ALGEBRA AND ITS APPLICATIONS, 517, 217 - 234, 03 , Refereed
  • Some norm inequalities for matrix means, Rajendra Bhatia, Yongdo Lim, Takeaki Yamazaki, LINEAR ALGEBRA AND ITS APPLICATIONS, LINEAR ALGEBRA AND ITS APPLICATIONS, 501, 112 - 122, 07 , Refereed
  • Equivalence relations among some inequalities on operator means, Wada, Shuhei, Yamazaki, Takeaki, Nihonkai Mathematical Journal, Nihonkai Mathematical Journal, 27, (1-2) 1 - 15, 06 , Refereed
  • Norm inequalities for matrix geometric means of positive definite matrices, Jun Ichi Fujii, Yuki Seo, Takeaki Yamazaki, LINEAR & MULTILINEAR ALGEBRA, LINEAR & MULTILINEAR ALGEBRA, 64, (3) 512 - 526, 03 , Refereed
  • On a family of operator means involving the power difference means, Yoichi Udagawa, Shuhei Wada, Takeaki Yamazaki, Masahiro Yanagida, LINEAR ALGEBRA AND ITS APPLICATIONS, LINEAR ALGEBRA AND ITS APPLICATIONS, 485, 124 - 131, 11 , Refereed
  • Some generalized numerical radius inequalities for Hilbert space operators, Mostafa Sattari, Mohammad Sal Moslehian, Takeaki Yamazaki, LINEAR ALGEBRA AND ITS APPLICATIONS, LINEAR ALGEBRA AND ITS APPLICATIONS, 470, 216 - 227, 04 , Refereed
  • Cartesian decomposition and numerical radius inequalities, Fuad Kittaneh, Mohammad Sal Moslehian, Takeaki Yamazaki, LINEAR ALGEBRA AND ITS APPLICATIONS, LINEAR ALGEBRA AND ITS APPLICATIONS, 471, 46 - 53, 04 , Refereed
  • A converse of Loewner-Heinz inequality and applications to operator means, Mitsuru Uchiyama, Takeaki Yamazaki, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 413, (1) 422 - 429, 05
  • An elementary proof of arithmetic-geometric mean inequality of the weighted Riemannian mean of positive definite matrices, Takeaki Yamazaki, LINEAR ALGEBRA AND ITS APPLICATIONS, LINEAR ALGEBRA AND ITS APPLICATIONS, 438, (4) 1564 - 1569, 02
  • THE RIEMANNIAN MEAN AND MATRIX INEQUALITIES RELATED TO THE ANDO-HIAI INEQUALITY AND CHAOTIC ORDER, Takeaki Yamazaki, OPERATORS AND MATRICES, OPERATORS AND MATRICES, 6, (3) 577 - 588, 09
  • Multi-variable weighted geometric means of positive definite matrices, Hosoo Lee, Yongdo Lim, Takeaki Yamazaki, LINEAR ALGEBRA AND ITS APPLICATIONS, LINEAR ALGEBRA AND ITS APPLICATIONS, 435, (2) 307 - 322, 07
  • On an elementary operator with w-hyponormal operator entries, M. Cho, S. V. Djordjevic, B. P. Duggal, T. Yamazaki, LINEAR ALGEBRA AND ITS APPLICATIONS, LINEAR ALGEBRA AND ITS APPLICATIONS, 433, (11-12) 2070 - 2079, 12
  • Weighted geometric mean of n-operators with n-parameters, Changdo Jung, Hosoo Lee, Yongdo Lim, Takeaki Yamazaki, LINEAR ALGEBRA AND ITS APPLICATIONS, LINEAR ALGEBRA AND ITS APPLICATIONS, 432, (6) 1515 - 1530, 03
  • On a new construction of geometric mean of n-operators, Changdo Jung, Hosoo Lee, Takeaki Yamazaki, LINEAR ALGEBRA AND ITS APPLICATIONS, LINEAR ALGEBRA AND ITS APPLICATIONS, 431, (9) 1477 - 1488, 10
  • ON A GEOMETRIC PROPERTY OF POSITIVE DEFINITE MATRICES CONE, Masatoshi Ito, Yuki Seo, Takeaki Yamazaki, Masahiro Yanagida, BANACH JOURNAL OF MATHEMATICAL ANALYSIS, BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 3, (2) 64 - 76
  • A remark on support of the principal function for class a operators, Muneo Cho, Mariko Giga, Tadasi Huruya, Takeaki Yamazaki, INTEGRAL EQUATIONS AND OPERATOR THEORY, INTEGRAL EQUATIONS AND OPERATOR THEORY, 57, (3) 303 - 308, 03
  • A remark on support of the principal function for class a operators, Muneo Cho, Mariko Giga, Tadasi Huruya, Takeaki Yamazaki, INTEGRAL EQUATIONS AND OPERATOR THEORY, INTEGRAL EQUATIONS AND OPERATOR THEORY, 57, (3) 303 - 308, 03
  • An extension of Kantorovich inequality to n-operators via the geometric mean by Ando-Li-Mathias, Takeaki Yamazaki, LINEAR ALGEBRA AND ITS APPLICATIONS, LINEAR ALGEBRA AND ITS APPLICATIONS, 416, (2-3) 688 - 695, 07
  • An operator transform from class A to the class of hyponormal operators and its application, M Cho, T Yamazaki, INTEGRAL EQUATIONS AND OPERATOR THEORY, INTEGRAL EQUATIONS AND OPERATOR THEORY, 53, (4) 497 - 508, 12
  • The iterated Aluthge transforms of a 2-by-2 matrix converge, T Ando, T Yamazaki, LINEAR ALGEBRA AND ITS APPLICATIONS, LINEAR ALGEBRA AND ITS APPLICATIONS, 375, 299 - 309, 12
  • On generalized numerical range of the Aluthge transformation, M Ito, H Nakazato, K Okubo, T Yamazaki, LINEAR ALGEBRA AND ITS APPLICATIONS, LINEAR ALGEBRA AND ITS APPLICATIONS, 370, 147 - 161, 09
  • On generalized numerical range of the Aluthge transformation, M Ito, H Nakazato, K Okubo, T Yamazaki, LINEAR ALGEBRA AND ITS APPLICATIONS, LINEAR ALGEBRA AND ITS APPLICATIONS, 370, 147 - 161, 09
  • On numerical range of the Aluthge transformation, T Yamazaki, LINEAR ALGEBRA AND ITS APPLICATIONS, LINEAR ALGEBRA AND ITS APPLICATIONS, 341, 111 - 117, 01

Misc

  • On the operator equation AB=zBA, Scientiae Mathematicae Japonicae,   2009
  • A remark on support of the principal function for class a operators, Muneo Cho, Mariko Giga, Tadasi Huruya, Takeaki Yamazaki, INTEGRAL EQUATIONS AND OPERATOR THEORY, 57, (3) 303 - 308,   2007 03 , Let T = U vertical bar T vertical bar be an invertible class A operator such that [ T*, T] is an element of C-1. Then we show that supp( g(T)) subset of sigma( T), where g(T) is the principal function of T. Moreover, we show that if T is pure, then supp( g(T)) = sigma( T).
  • On upper and lower bounds of the numerical radius and an equality condition, Studia Mathematica,   2007
  • An extension of Kantorovich inequality to n-operators via the geometric mean by Ando-Li-Mathias, Linear Algebra and its Applications,   2006
  • On conparisons of norms and the numerical ranges of an operator with its generalized Aluthge transformation, Scientiae Mathematicae Japonicae,   2005
  • An operator transform from class A to the class of hyponormal operators and its application, Integral Equations Operator Theory, Vol. 53 (2005).,   2005
  • On numerical range and norm of the generalized Aluthge transform,   2005
  • On single-valued extension property and Bishop's one of class A operators,   2004
  • On the polar decomposition of the product of two operators and its applications, Integral Equations Operator Theory, vol. 49,   2004
  • On the polar decomposition of the Aluthge transformation and related results, J. Operator Theory, Vol. 51,   2004
  • Mosaic and principal functions of log-hyponormal operators,   2004
  • Weakly chaotic order and its application to class A operators,   2004
  • On the polar decomposition of the product of operators,   2004
  • On some norm inequalities associated with the variance of an operator,   2004
  • On numerical range and norm of the generalized Aluthge transform,   2004
  • The iterated Aluthge transforms of a 2-by-2 matrix converge, T Ando, T Yamazaki, LINEAR ALGEBRA AND ITS APPLICATIONS, 375,   2003 12 , The Aluthge transform of a square complex matrix T with polar representation T = U\T\ is by definition Delta(T) equivalent to \T\U-1/2\T\(1/2). It has been conjectured that the iterates Delta(T), Delta(Delta (T)), . . . converge. We prove this when T is a 2-by-2 matrix. (C) 2003 Elsevier Inc. All rights reserved.
  • On generalized numerical range of the Aluthge transformation, M Ito, H Nakazato, K Okubo, T Yamazaki, LINEAR ALGEBRA AND ITS APPLICATIONS, 370,   2003 09 , In this paper the authors show that the Aluthge transformation (T) over tilde of a matrix T and a polynomial f satisfy the inclusion relation W-C (f((T) over tilde)) subset of W-C (f(T)) for the generalized numerical range if C is a Hermitian matrix or a rank-one matrix. (C) 2003 Elsevier Inc. All rights reserved.
  • On generalized numerical range of the Aluthge transformation,   2003
  • The polar decomposition of the operators and its applications to binormal and centered operators,   2003
  • Operator inequalities derived from new formula that Specht ratioS(1) can be expressed by generalized Kantorovich constant K(p): S(1)=e^K'(1),   2003
  • An operator transform from class A to the class of hyponormal operators,   2003
  • Relations among operator inequalities following from log Ageq log B,   2003
  • Relations among operator orders and operator inequalities,   2003
  • An operator transform from class A to the class of hyponormal operators and its application,   2003
  • An operator transform from class A to the class of hyponormal operators,   2003
  • On approximate point joint spectrum of p-hyponormal and log-hyponormal operators, Comment. Math. Prace Mat., 43(2003),   2003
  • Relations between two operator inequalities and their applications to paranormal operators, Acta Sci. Math. (Szeged), 69(2003),   2003
  • Generalizations of results on relations between Furuta-type inequalities, Acta Math Sci. (Szeged), 69(2003),   2003
  • On generalized numerical range of the Aluthge transformation, Linear Algebra Appl., 370(2003),   2003
  • On the polar decompositions of Aluthge transformation and powers of operators,   2002
  • Generalizations of results on relations between Furuta-type inequalities,   2002
  • Properties of Aluthge transformation on operator norms, The 6th workshop on numerical range and numerical radius, Auburn University,   2002
  • Relations between two Furuta-type inequalities, The 10th ILAS conference, Auburn University,   2002
  • On binormality of the Aluthge transformation,   2002
  • On a relation between the polar decomposition and commutativity of operators,   2002
  • Relations between two inequalities (B^fracr2A^pB^fracr2)^fracrp+rgeq B^r and A^pgeq (A^fracp2A^rA^fracp2)^fracpp+r and their applications, Integral Equations Operator Theory, 44(2002).,   2002
  • Characterizations of log Ageq log B and normaloid operators via Heinz inequality, Integral Equations Operator Theory, 43(2002),   2002
  • An expression of spectral radius via Aluthge transformation, Proc. Amer. Math. Soc., 130(2002),   2002
  • On numerical range of the Aluthge transformation, Linear Algebra Appl.,341(2002),   2002
  • Order prederving operator inequalities associated with Kantorovich inequality and Specht's theorem,   2001
  • Several properties of Aluthge transformation,   2001
  • Several properties of Aluthge transformation,   2001
  • Order preserving operator inequalities and Aluthge transformation, KOTAC 2001 Operator theory and its applications, Cheju National University,   2001
  • On numerical range of the Aluthge transformation,   2001
  • Relations between two operator inequalities and their applications to paranormal operators,   2001
  • Relations between two inequalities (B^fracr2A^pB^fracr2)^fracrp+r ge B^r and A^p ge (A^fracp2B^rA^fracp2)^fracpp+r and their applications,   2001
  • Relations between two operator inequalities and their applications to paranormal operators,   2001
  • On numerical range and polar decomposition of the Aluthge transformation,   2001
  • Relations between two inequalities (B^fracr2A^pB^fracr2)^fracrp+r ge B^r and A^p ge (A^fracp2B^rA^fracp2)^fracpp+r and their applications,   2001
  • parallelism between Aluthge transformation and powers of operators, Acta Sci. Math. (Szeged),67(2001),   2001
  • Several properties on Aluthge transformation,   2001
  • Characterizations of chaoric order associated with Kantorovich inequality,   2000
  • a characterization of log-hyponormal operators via p-paranormality, Scientiae Mathematicae vol.3,   2000
  • An extension of Specht's theorem via Kantorovich inequality and related results, T Yamazaki, MATHEMATICAL INEQUALITIES & APPLICATIONS, 3, (1) 89 - 96,   2000 01 , In this paper, we shall show the following result. "If MI greater than or equal to A greater than or equal to ml > 0 with M > m > 0, then K+(m(r), M-r, p/r)(1/p)(A(r)x, x)(1/r) greater than or equal to (A(p)x, x)(1/p) for p > r > 0, where K+(m, M, p) = (p-1)(p-1)/p(p) (M-p-m(p))(p)/(M-m)(mM(p)-Mm(p))(p-1)". This result is an extension of Specht's theorem [6] as a converse of the arithmetic-geometric mean inequality. "If x(1), x(2), ..., x(n) is an element of [m, M] with M > m > 0, then M-h (n)root x(1)x(2)...x(n) greater than or equal to x(1)+x(2)+...+x(n)/n where h = M/m > 1 and M-h = h(1/h-1)/e log h(1/h-1)". Secondly, we shall show an application for operator inequalities, that is, "if A greater than or equal to B greater than or equal to 0 satisfying MI greater than or equal to B greater than or equal to ml > 0 with M > m > 0, then A(p) - B-p greater than or equal to -(mM(p)-Mm(p))/M-m {K+(m,M,p)(1/p-1)-1} for p > 1.".
  • Further extensions of characterizations of chaotic order associated with Kantorovich type inequalities, Scientiae Mathematicae.Vol.3,   2000
  • Further extension of characterizations of chaotic order associated with Kantorovich type inequalities,   2000
  • Extensions of paranormal operators and their properties,   2000
  • A further generalization of paranormal operators, Scientiae Mathematicae vol.3,   2000
  • Further extensions of characterizations of chaotic order associated with Kantorovich type inequalities,   2000
  • Priperties on several classis including log-hyponormal operators,   2000
  • On powers of p-hyponormal and log-hyponormal operators,   2000
  • Order prederving operator inequalities associated with Kantorovich inequality and Specht's ratio,   2000
  • Order prederving operator inequalities and related results,   2000
  • On powers of class A(k) operators including p-hyponormal and log-hyponormal operators,   2000
  • Recent applications of order preserving operator inequalities,   2000
  • On powers of class A(k) operators including p-hyponormal and log-hyponormal operators,   2000
  • Further extensions of characterizations of chaotic order associated with Kantorovich type inequalities,   2000
  • Extensions of paranormal operators and their properties,   2000
  • On powers of class A(k) operators including p-hyponormal and log-hyponormal operators,,   2000
  • Extensions of paranormal operators and their properties,,   2000
  • Further extensions of characterizations of chaotic order associated with Kantorovich type inequalities,,   2000
  • Further characterizations of chaotic order via Specht's ratio, Math.Inequal.Appl.,   2000
  • Order prederving operator inequalities associated with Kantorovich inequality and Specht's ratio,   2000
  • Order prederving operator inequalities associated with Kantorovich inequality and Specht's ratio,   2000
  • Order prederving operator inequalities associated with Kantorovich inequality and Specht's ratio,   2000
  • Several properties on Aluthge transformation,   2000
  • Order prederving operator inequalities and related results,   2000
  • Several properties of Aluthge transformation,   2000
  • On powers of class A( ) operators including p-hyponormal and log-hyponormal Operators, Mathematical Inequalities and Applications vol.3,   2000
  • Simplified proof of characterization of chaotic order via Specht's ratio, Scientiae Mathematicae vol.2,   1999
  • Extensions of teh results on p-hyponormal and log-hyponormal operators by Aluthge and Wang, SUT Journal of Mathematics vol.35,   1999
  • Simplified proof of Tanahashi's result on the best possibility of generalized Furuta inequality, Mathematical Inequalities and Applications vol.2,   1999
  • Characterizations of chaotic Order assosciated with Kantorovich inequality, Scientiae Mathematicae vol.2,   1999
  • A subclass of paranormal including class of log-hyponormal and several related classes,   1999
  • Characterizations of chaotic order associated with Kantorovich inequality,   1999
  • Characterizations of chaoric order associated with Kantorovich inequality,   1999
  • A subclass of paranormal including class of log-hyponormal and several related classes,   1999
  • Characterizations of chaoric order associated with Kantorovich inequality,   1999
  • A simplified proof of Tanahashi's result on the best possibility of generalized Furuta inequality,   1999
  • Order preserving operator inequalities and their recent applications,   1999
  • Extensions of the results on p-hyponormal and log-hyponormal operators by Aluthge and Wang,   1999
  • Properties on several classes including log-hyponormal operators,   1999
  • Further extensions of characterizations of chaotic order associated with Kantorovich type inequalities,   1999
  • On powers of p-hyponormal and log-hyponormal operators,   1999
  • An extension of order preserving operator inequalities,   1998
  • Generalized operator functions implying order preserving operator inequalities,   1998
  • Equivalence relations among Furuta-type inequalities with negative pwoers, Scientiae Mathematicae vol.1,   1998
  • A subclass of paranormal operators including class of log-hyponormal and several related classes, Scientiae Mathematicae vol.1,   1998
  • On order preserving inequalities with negative powers and a related conjecture,   1998
  • Order preserving operator inequalities via Furuta inequality, Mathematica Japonica vol.48,   1998
  • Operator functions implying generalized Furuta inezuality, Mathematical Inequalities and Applications vol.1,   1998
  • A subclass of paranormal including class of log-hyponormal,   1998
  • On a conjecture related to Furuta-type inequalities with negative powers, Nihonkai Mathematical Journal vol.9,   1998
  • Generalized operator functions implying order preserving operator inequalities,   1998
  • Order preserving operator inequalities via Furuta inequality,   1998
  • Order preserving inequality associated with H"older-McCarthy and Kantorovich inequalities,   1998
  • Equivalence relations among order preserving operator inequalities and a related open problem,   1998
  • A conjecture on order preserving operator inequalities and related equivalence relations,   1998
  • Generalized operator functions implying order preserving inequalities,   1998
  • On order preserving inequalities with negative powers and a related conjecture,   1998
  • A subclass of paranormal including class of log-hyponormal,   1998
  • Order preserving inequality associated with H"older-McCarthy and Kantorovich inequalities,   1998
  • A subclass of paranomal including class of log-hyponormal and severalrelated classes,   1998
  • A characterization of chaotic order associated with Kantorovich inequality,   1998
  • Characterizations of chaotic order associated with Kantorovich inequality,   1998
  • A subclass of paranormal including class of log-hyponormal and several related classes,   1998
  • Characterizations of chaotic order associated with Kantorovich inequality,   1998
  • A subclass of paranormal including class of log-hyponormal and several related class,   1998
  • Order preserving operator inequalities via Furuta inequality,   1997
  • Operator functions implying order preserving inequalities,,   1997
  • An order preserving operator inequality,   1997
  • Generalized operator functions implying order preserving operator inequalities,   1997
  • An extension of order preserving operator inequalities,   1997
  • Equivalence relations among order preserving operator inequalities and a related open problem,   1997
  • Generalized operator functions implying order preserving operator inequalities,   1997

Conference Activities & Talks

  • Power monotonicity for a path of operator means, YAMAZAKI TAKEAKI, International conference on Matrix Theory and Applications,   2019 05 24 , Invited
  • Generalized Karcher equation, operator entropy and the Ando-Hiai ineuqlaity, YAMAZAKI TAKEAKI, Mathematical inequalities and Applications Conference 2018,   2018 07 06
  • Generalized Karcher equations, operator entropies, and extensions, YAMAZAKI TAKEAKI, 2017 Korea-China International Conference on Matrix Theory with Applications,   2017 12 15 , Invited
  • Properties of weighted operator means via generalized relative operator entropy, YAMAZAKI TAKEAKI, ILAS 2017,   2017 07 24 , Invited
  • Some norm inequality for matrix means, YAMAZAKI TAKEAKI, YT004484,   2017 03 25
  • Some norm inequalities for matrix means, YAMAZAKI TAKEAKI, MATRIX THEORY AND RELATED TOPICS,   2016 12 29 , Invited
  • Some norm inequalities for matrix means, YAMAZAKI TAKEAKI,   2016 11 10
  • Some recent topics on operator means, YAMAZAKI TAKEAKI, YT004484,   2016 09 03 , Invited
  • Characterizations of the interpolational means and an application, YAMAZAKI TAKEAKI, 20th ILAS Conference,   2016 07 13 , Invited
  • On interpolational means and an application, YAMAZAKI TAKEAKI, 2016 International workshop on matrix inequalities and matrix equations,   2016 06 10 , Invited
  • Research of weighted operator means from two points of view, YAMAZAKI TAKEAKI,   2015 11 10
  • On properties of weighted operator means due to Palfia and Petz, YAMAZAKI TAKEAKI,   2015 10 25 , Invited
  • Some properties of weighted operator means due to Palfia and Petz, UDAGAWA YOICHI, YAMAZAKI TAKEAKI, YANAGIDA MASAHIRO,   2015 09 15
  • Some properties of weighted operator means due to Palfia and Petz, YAMAZAKI TAKEAKI, Workshop on Quantum Information Theory and Related Topics,   2015 09 01 , Invited
  • Some operator inequalities on operator means, YAMAZAKI TAKEAKI, Workshop on function spaces, harmonic analysis and related topics,   2015 04 27
  • Equivalence relations among some inequalities on operator means, YAMAZAKI TAKEAKI, WADA SHUHEI,   2014 11 27
  • A converse of Loewner-Heinz inequality and applications to operator means, YAMAZAKI TAKEAKI, 19th ILAS Conference,   2014 08 09
  • Generalized Ando-Hiai inequality for matrix power mean, YAMAZAKI TAKEAKI,   2014 03 18
  • On geometric mean of n-matrices and related results, YAMAZAKI TAKEAKI, The 7th Seminar on Linear Algebra and its Applications,   2014 02 26 , Invited
  • Operator inequality and Operator mean, YAMAZAKI TAKEAKI, Mathematical Society of Japan,   2013 09 27 , Invited