19 Result(s)
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Chapter
Maximal f-Divergences
Let M be a von Neumann algebra with its standard form ( M , ℋ , ...
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Chapter
Introduction
The notion of quantum divergences has played a significant role in quantum information, which defines important quantum quantities to discriminate between states of a quantum system. A quantum system is mathem...
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Chapter
Reversibility and Quantum Divergences
Let M and N be von Neumann algebras, whose standard forms are ( M , ℋ ...
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Chapter
Preservation of Maximal f-Divergences
In this chapter we will characterize the preservation of ...
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Chapter
Rényi Divergences and Sandwiched Rényi Divergences
Let M be a general von Neumann algebra given in a standard form ( M , ℋ ...
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Chapter
Measured f-Divergences
Let f be a convex function on (0, ∞), not necessarily operator convex unless we specify that. We use the convention in (2.2). Let M be a general von Neumann algebra. A m...
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Chapter
Reversibility and Measurements
This chapter is concerned with the approximate reversibility (sufficiency) for a sequence of quantum operations α k : M k → M (or quantum channels with input M and outputs M k). Our main problem is to characteriz...
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Chapter
Standard f-Divergences
Let M be a general von Neumann algebra, and M ...
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Chapter
Matrix Limit Theorems of Kato Type Related to Positive Linear Maps and Operator Means
We obtain limit theorems for \(\Phi (A^p)^{1/p}\) Φ ( A p ) 1 / p and \((A^p\sigma B)^{1/p}\) ( A p σ B ) 1 / p as \(p\rightarrow \infty \) p → ∞ for positive matrices A, B, where
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Chapter
A Appendices
A.1 Non-symmetric means
A.2 Norm inequality for operator integrals
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Chapter
References
Abstract not available
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Chapter
2 Double integral transformations
2.1 Schur multipliers and Peller’s theorem
2.2 Extension to B(H)
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Chapter
4 Convergence of means
4.1 Main convergence result
4.2 Related convergence results
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Chapter
6 Heinz-type means A α
6.1 Norm continuity in parameter
6.2 Convergence of operator Riemann sums
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Chapter
8 Certain alternating sums of operators
8.1 Preliminaries
8.2 Uniform bounds for norms
8.3 Mono...
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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...
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Chapter
3 Means of operators and their comparison
3.1 Symmetric homogeneous means
3.2 Integral expression and comparison of norms
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Chapter
5 A-L-G interpolation means M α
5.1 Monotonicity and related results
5.2 Characterization of |||M ∞(H,K)X<∞
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Chapter
7 Binomial means B α
7.1 Majorization B α⪯M ∞
7.2 Equivalence of |||B α (H,K)X||| for
