Fumio Hiai

Profile Information

Degree: 理学博士(東京工業大学)

J-GLOBAL ID: 200901059750925190
researchmap Member ID: 1000008235

External link: http://db.tohoku.ac.jp/whois/detail/340f360473ce9efb66b08f86f84572e5.html

Research Interests

Research Areas

Research History

1990 - 1998

Ibaraki University
1990 - 1998

Ibaraki University, Professor
1985 - 1990

Hokkaido University
1985 - 1990

Hokkaido University, Assistant Professor
1984 - 1985

Tokyo University of Science
1984 - 1985

Science University of Tokyo, Assistant Professor
1976 - 1984

Tokyo University of Science
1976 - 1984

Science University of Tokyo, Lecturer
1975 - 1976

Tokyo Institute of Technology
1975 - 1976

Tokyo Institute of Technology, Research Assistant
Professor, Tohoku University Graduate School of Information Sciences, Department of System Information Sciences

Education

Misc.

234

QUANTUM f-DIVERGENCES AND ERROR CORRECTION

Fumio Hiai, Milan Mosonyi, Denes Petz, Cedric Beny

REVIEWS IN MATHEMATICAL PHYSICS, 23(7) 691-747, Aug, 2011
NORM AND ANTI-NORM INEQUALITIES FOR POSITIVE SEMI-DEFINITE MATRICES

Jean-Christophe Bourin, Fumio Hiai

INTERNATIONAL JOURNAL OF MATHEMATICS, 22(8) 1121-1138, Aug, 2011
QUANTUM f-DIVERGENCES AND ERROR CORRECTION

Fumio Hiai, Milan Mosonyi, Denes Petz, Cedric Beny

REVIEWS IN MATHEMATICAL PHYSICS, 23(7) 691-747, Aug, 2011
NORM AND ANTI-NORM INEQUALITIES FOR POSITIVE SEMI-DEFINITE MATRICES

Jean-Christophe Bourin, Fumio Hiai

INTERNATIONAL JOURNAL OF MATHEMATICS, 22(8) 1121-1138, Aug, 2011
Operator log-convex functions and operator means

Tsuyoshi Ando, Fumio Hiai

MATHEMATISCHE ANNALEN, 350(3) 611-630, Jul, 2011
Operator log-convex functions and operator means

Tsuyoshi Ando, Fumio Hiai

MATHEMATISCHE ANNALEN, 350(3) 611-630, Jul, 2011
On the Quantum Renyi Relative Entropies and Related Capacity Formulas

Milan Mosonyi, Fumio Hiai

IEEE TRANSACTIONS ON INFORMATION THEORY, 57(4) 2474-2487, Apr, 2011
On the Quantum Renyi Relative Entropies and Related Capacity Formulas

Milan Mosonyi, Fumio Hiai

IEEE TRANSACTIONS ON INFORMATION THEORY, 57(4) 2474-2487, Apr, 2011
Higher order extension of L"owner's theory: Operator k-tone functions

日合文雄

作用素論・作用素環論研究集会報告集, 59-68, 2011
Higher order extension of L"owner's theory: Operator k-tone functions

Fumio Hiai

作用素論・作用素環論研究集会報告集, 59-68, 2011
Strongly subadditive functions

K. Audenaert, F. Hiai, D. Petz

ACTA MATHEMATICA HUNGARICA, 128(4) 386-394, Sep, 2010
Strongly subadditive functions

K. Audenaert, F. Hiai, D. Petz

ACTA MATHEMATICA HUNGARICA, 128(4) 386-394, Sep, 2010
Matrix Analysis: Matrix Monotone Functions, Matrix Means, and Majorization

F. Hiai

Interdisciplinary Information Sciences, 16(2) 139-246, 2010
A new approach to mutual information. II

F. Hiai, T. Miyamoto

Banach Center Publications, 89 143-163, 2010
正定値行列の空間における平均と関連するRiemann計量

日合文雄

数理解析研講究録「作用素論における非可換解析学の展望」, 1678 55-73, 2010
Matrix Analysis: Matrix Monotone Functions, Matrix Means, and Majorization

F. Hiai

Interdisciplinary Information Sciences, 16(2) 139-246, 2010
A new approach to mutual information. II

F. Hiai, T. Miyamoto

Banach Center Publications, 89 143-163, 2010
Riemannian metrics in the space of positive definite matrices related to means

Fumio Hiai

Surikaisekiken-Kokyuroku, 1678 55-73, 2010
Quantum hypothesis testing with group symmetry

Fumio Hiai, Milan Mosonyi, Masahito Hayashi

JOURNAL OF MATHEMATICAL PHYSICS, 50(10) 103304, Oct, 2009
Monotonicity for entrywise functions of matrices

Fumio Hiai

LINEAR ALGEBRA AND ITS APPLICATIONS, 431(8) 1125-1146, Sep, 2009

Books and Other Publications

Means of Hilbert Space Operators (Lecture Notes in Mathematics, Vol. 1820)

Springer-Verlag, 2003
Means of Hilbert Space Operators (Lecture Notes in Mathematics, Vol. 1820)

Springer-Verlag, 2003
The Semicircle Law, Free Random Variables and Entropy

Amer. Math. Soc., 2000
The Semicircle Law, Free Random Variables and Entropy

Amer. Math. Soc., 2000
ヒルベルト空間と線型作用素

牧野書店, 1995
Hilbert Spaces and Linear Operators

牧野書店, 1995
作用素代数入門

共立出版, 1985
Introduction to Operator Algebras

共立出版, 1985

Presentations

Convexity of quasi-entropy type functions: Lieb's and Ando's convexity theorems revisited

The 6th Jikji Workshop: Infinite Dimensional Analysis and Quantum Probability, 2011
Generalizing Minkowski's determinantal inequality (joint work with J.-C. Bourin)

International Conference "Product Systems and Independence in Quantum Dynamics", 2011
Free energy density in one-dimensional spin chains

Summer school on "Non-equilibrium statistical mechanics", 2011
Jensen and Minkowski type inequalities for operator means (joint work with J.-C. Bourin)

14th Workshop "Non-commutative Harmonic Analysis", 2011
Convexity of quasi-entropy type functions: Lieb's and Ando's convexity theorems revisited

The 6th Jikji Workshop: Infinite Dimensional Analysis and Quantum Probability, 2011
Generalizing Minkowski's determinantal inequality (joint work with J.-C. Bourin)

International Conference "Product Systems and Independence in Quantum Dynamics", 2011
Free energy density in one-dimensional spin chains

Summer school on "Non-equilibrium statistical mechanics", 2011
Jensen and Minkowski type inequalities for operator means (joint work with J.-C. Bourin)

14th Workshop "Non-commutative Harmonic Analysis", 2011
Operator log-convex functions and operator means (joint work with T. Ando)

The 16th Conference of the International Linear Algebra Society, 2010
Riemannian metrics on positive definite matrices related to means (joint work with Denes Petz)

Information Geometry and its Applications III, 2010
Operator log-convexity and its applications

Program: Quantum Information Theory, 2010
Operator log-convex functions and operator means (joint work with T. Ando)

The 16th Conference of the International Linear Algebra Society, 2010
Riemannian metrics on positive definite matrices related to means (joint work with Denes Petz)

Information Geometry and its Applications III, 2010
Operator log-convexity and its applications

Program: Quantum Information Theory, 2010
Riemannian metrics on positive definite matrices related to means (joint work with D. Petz)

12th Workshop "Non-commutative Harmonic Analysis", 2009
Riemannian metrics on positive definite matrices related to means (joint work with D. Petz)

12th Workshop "Non-commutative Harmonic Analysis", 2009
Free pressure, free entropy and hypothesis testing

Workshop "Free Probability, Extensions, and Applications", 2008
Pressure and its Legendre transform in microstate free entropy

11th Workshop "Non-commutative Harmonic Analysis with Applications to Probability", 2008
Mutual information and mutual pressure

Conference "Information and Communication", 2008
Orbital approach to free entropy and free pressure

2008 Global Korean Mathematical Society International Conference, 2008

Professional Memberships

Works

量子情報理論と量子確率論の新展開

2008 - 2010
量子情報理論と量子確率論の新展開

2008 - 2010
自由確率論とランダム行列 -- 新しい情報数理に向けて

2004 - 2006
自由確率論とランダム行列 -- 新しい情報数理に向けて

2004 - 2006

Profile Information

Research Interests

Research Areas

Research History

Education

Misc.

Books and Other Publications

Presentations

Professional Memberships

Works

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