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within Mathematics Remove this filter Linear and Multilinear Algebras, Matrix Theory Remove this filter Fumio Hiai Remove this filter Chapter Remove this filter

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  1. No Access

    Chapter

    Fundamentals of Operators and Matrices

    A linear map** is essentially a matrix if the vector space is finite-dimensional. In this book the vector space is typically a finite-dimensional complex Hilbert space.

    Fumio Hiai, Dénes Petz in Introduction to Matrix Analysis and Applications (2014)

  2. No Access

    Chapter

    Functional Calculus and Derivation

    Let \(A\in \mathbb {M}_n({\mathbb C})\) A ∈ ...

    Fumio Hiai, Dénes Petz in Introduction to Matrix Analysis and Applications (2014)

  3. No Access

    Chapter

    Matrix Means and Inequalities

    The study of numerical means has been a popular subject for centuries, and the inequalities

    Fumio Hiai, Dénes Petz in Introduction to Matrix Analysis and Applications (2014)

  4. No Access

    Chapter

    Some Applications

    Matrices are important in many areas of both pure and applied mathematics. In particular, they play essential roles in quantum probability and quantum information.

    Fumio Hiai, Dénes Petz in Introduction to Matrix Analysis and Applications (2014)

  5. No Access

    Chapter

    Map**s and Algebras

    Most of the statements and definitions in this chapter are formulated in the Hilbert space setting.

    Fumio Hiai, Dénes Petz in Introduction to Matrix Analysis and Applications (2014)

  6. No Access

    Chapter

    Matrix Monotone Functions and Convexity

    Let \((a, b) \subset {\mathbb R}\) ( a , ...

    Fumio Hiai, Dénes Petz in Introduction to Matrix Analysis and Applications (2014)

  7. No Access

    Chapter

    Majorization and Singular Values

    A citation from von Neumann: “The object of this note is the study of certain properties of complex matrices of \(n\) ...

    Fumio Hiai, Dénes Petz in Introduction to Matrix Analysis and Applications (2014)

  8. No Access

    Chapter

    A Appendices

  9. A.1 Non-symmetric means

  10. A.2 Norm inequality for operator integrals

  11. ...

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

  12. No Access

    Chapter

    References

    Abstract not available

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

  13. No Access

    Chapter

    2 Double integral transformations

  14. 2.1 Schur multipliers and Peller’s theorem

  15. 2.2 Extension to B(H)

  16. ...

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

  17. No Access

    Chapter

    4 Convergence of means

  18. 4.1 Main convergence result

  19. 4.2 Related convergence results

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

  20. No Access

    Chapter

    6 Heinz-type means A α

  21. 6.1 Norm continuity in parameter

  22. 6.2 Convergence of operator Riemann sums

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

  23. No Access

    Chapter

    8 Certain alternating sums of operators

  24. 8.1 Preliminaries

  25. 8.2 Uniform bounds for norms

  26. 8.3 Mono...

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

  27. 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)

  28. No Access

    Chapter

    3 Means of operators and their comparison

  29. 3.1 Symmetric homogeneous means

  30. 3.2 Integral expression and comparison of norms

    31. ...

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

  31. No Access

    Chapter

    5 A-L-G interpolation means M α

  32. 5.1 Monotonicity and related results

  33. 5.2 Characterization of |||M ∞(H,K)X<∞

    34. ...

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

  34. No Access

    Chapter

    7 Binomial means B α

  35. 7.1 Majorization B α⪯M ∞

  36. 7.2 Equivalence of |||B α (H,K)X||| for

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