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- Name
- HIAI Fumio
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- Affiliation
- Graduate School of Information Sciences
Department of System Information Sciences
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- Title
- Professor
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- Date of Birth
- 1948.3
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Research Fields
- Global analysis（Operator）
- Basic analysis（Operator Theoty）
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Research Subjects
- Operator algebra (1980-)
- Operator theory (1987-)
- Noncommutative probability theory (1980-)
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- Keywords
- Operator algebra, Operator theory, Noncommutative Probability theory
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- Books
- Introduction to Operator Algebras.[共立出版,(1985)] 梅垣壽春，大矢雅則，日合文雄
- Hilbert Spaces and Linear Operators.[牧野書店,(1995)] 日合文雄，柳研二郎
- The Semicircle Law, Free Random Variables and Entropy.[Amer. Math. Soc.,(2000)] F. Hiai and D. Petz
- Means of Hilbert Space Operators (Lecture Notes in Mathematics, Vol. 1820).[Springer-Verlag,(2003)] F. Hiai and H. Kosaki
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- Original Papers
- Integrals, conditional expectations, and martingales of multivalued functions.[J. Multivariate Analysis,7,(1977),149-182] F. Hiai and H. Umegaki
- Minimizing indices of conditional expectations onto a subfactor.[Publ. Res. Inst. Math. Sci.,24,(1988),673-678] F. Hiai
- The proper formula for relative entropy and its asymptotics in quantum probability.[Comm. Math. Phys.,143,(1991),99-114] F. Hiai and D. Petz
- Amenability and strong amenability for fusion algebras with applications to subfactor theory.[Internat. J. Math.,9,(1998),669-722] F. Hiai and M. Izumi
- Log majorization and complementary Golden-Thompson type inequalities.[Linear Algebra Appl.,197/198,(1994),113-131] T. Ando and F. Hiai
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- Review Papers
- 確率論のパラレルワールド -- 自由確率論.[日本数学会年会, 企画特別講演アブストラクト,(2002),38-49] 日合文雄
- Free relative entropy and q-deformation theory.[World Scientific Non-Commutativity, Infinite-Dimensionality and Probability at the Crossroads, N. Obata et al. (eds.), QP-PQ,16,(2002),97-142] F. Hiai
- Operator means and their norms.[Mathematical Society of Japan Advanced Studies in Pure Mathematics, H. Kosaki (ed.),38,(2004),271-284] F. Hiai and H. Kosaki
- Random matrices and free probability theory.[Yuseisha Invitation to Mathematical Physics,6,(2006),121-147] F. Hiai and Y. Ueda
- Orbital approach to free entropy and free entropy dimension.[Surikaisekiken-Kokyuroku,1534,(2007),51-66] F. Hiai
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- Web Site
- http://math.is.tohoku.ac.jp/
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- Updated on
- 2008.03.25
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