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  1. No Access

    Chapter and Conference Paper

    Strong laws of large numbers for multivalued random variables

    Fumio Hiai in Multifunctions and Integrands (1984)

  2. No Access

    Article

    Majorizations for generalizeds-numbers in semifinite von Neumann algebras

    Fumio Hiai, Yoshihiro Nakamura in Mathematische Zeitschrift (1987)

  3. No Access

    Article

    The proper formula for relative entropy and its asymptotics in quantum probability

    Umegaki's relative entropyS(ω,ϕ)=TrD ω(logD ω−logD ϕ) (of states ω and ϕ with density operatorsD ω andD ϕ, respectively) is shown to be an asymptotic exponent considered from the quantum hypothesis testing viewpo...

    Fumio Hiai, Dénes Petz in Communications in Mathematical Physics (1991)

  4. No Access

    Chapter

    L p -Distance between Unitary Orbits in Type IIIλ Factors

    Let M bea factor of type IIIλ*, 0 < λ < 1, and , 1 ≤ p ≤ ∞, the discrete Haagerup L p spaces. We obtain the L p -distance ...

    Fumio Hiai, Yoshihiro Nakamura in Contributions to Operator Theory and its Applications (1993)

  5. No Access

    Article

    Trace norm convergence of exponential product formula

    LetH andK be lower-bounded self-adjoint operators whose form sum is denoted byH \(\hat + \) K. We show the norm in...

    Fumio Hiai in Letters in Mathematical Physics (1995)

  6. No Access

    Article

    McMillan type convergence for quantum Gibbs states

    Fumio Hiai, Masanori Ohya, Dénes Petz in Archiv der Mathematik (1995)

  7. No Access

    Article

    Properties of Free Entropy Related to Polar Decomposition

    The free entropies of non-selfadjoint random variables and of unitary random variables are introduced and discussed by the methods of V...

    Fumio Hiai, Dénes Petz in Communications in Mathematical Physics (1999)

  8. No Access

    Book

    Means of Hilbert Space Operators

    Fumio Hiai, Hideki Kosaki in Lecture Notes in Mathematics (2003)

  9. No Access

    Chapter

    A Appendices

  10. A.1 Non-symmetric means

  11. A.2 Norm inequality for operator integrals

  12. ...

    13. Fumio Hiai, Hideki Kosaki in Means of Hilbert Space Operators (2003)

  13. No Access

    Chapter

    References

    Abstract not available

    Fumio Hiai, Hideki Kosaki in Means of Hilbert Space Operators (2003)

  14. No Access

    Chapter

    2 Double integral transformations

  15. 2.1 Schur multipliers and Peller’s theorem

  16. 2.2 Extension to B(H)

  17. ...

    18. Fumio Hiai, Hideki Kosaki in Means of Hilbert Space Operators (2003)

  18. No Access

    Chapter

    4 Convergence of means

  19. 4.1 Main convergence result

  20. 4.2 Related convergence results

    21. Fumio Hiai, Hideki Kosaki in Means of Hilbert Space Operators (2003)

  21. No Access

    Chapter

    6 Heinz-type means A α

  22. 6.1 Norm continuity in parameter

  23. 6.2 Convergence of operator Riemann sums

    24. Fumio Hiai, Hideki Kosaki in Means of Hilbert Space Operators (2003)

  24. No Access

    Chapter

    8 Certain alternating sums of operators

  25. 8.1 Preliminaries

  26. 8.2 Uniform bounds for norms

  27. 8.3 Mono...

    28. Fumio Hiai, Hideki Kosaki in Means of Hilbert Space Operators (2003)

  28. No Access

    Chapter

    1 Introduction

    The present monograph is devoted to a thorough study of means for Hilbert space operators, especially comparison of (unitarily invariant) norms of operator means and their convergence properties in various asp...

    Fumio Hiai, Hideki Kosaki in Means of Hilbert Space Operators (2003)

  29. No Access

    Chapter

    3 Means of operators and their comparison

  30. 3.1 Symmetric homogeneous means

  31. 3.2 Integral expression and comparison of norms

    32. ...

    Fumio Hiai, Hideki Kosaki in Means of Hilbert Space Operators (2003)

  32. No Access

    Chapter

    5 A-L-G interpolation means M α

  33. 5.1 Monotonicity and related results

  34. 5.2 Characterization of |||M ∞(H,K)X<∞

    35. ...

    Fumio Hiai, Hideki Kosaki in Means of Hilbert Space Operators (2003)

  35. No Access

    Chapter

    7 Binomial means B α

  36. 7.1 Majorization B α⪯M ∞

  37. 7.2 Equivalence of |||B α (H,K)X||| for

    38. Fumio Hiai, Hideki Kosaki in Means of Hilbert Space Operators (2003)

  38. Article

    Free transportation cost inequalities via random matrix approximation

    By means of random matrix approximation procedure, we re-prove Biane and Voiculescu’s free analog of Talagrand’s transportation cost inequality for measures on R in a more general setup. Furthermore, we prove the...

    Fumio Hiai, Dénes Petz, Yoshimichi Ueda in Probability Theory and Related Fields (2004)

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    Article

    Free Analog of Pressure and Its Legendre Transform

    The free analog of the pressure is introduced for multivariate noncommutative random variables and its Legendre transform is compared with Voiculescu’s microstate free entropy.

    Fumio Hiai in Communications in Mathematical Physics (2005)

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