Eigenvalue inequalities for convex and log-convex functions
TLDR
In this paper, a matrix version of Choi's inequality for positive unital maps and operator convex functions remains valid for monotone convex function at the cost of unitary congruences.About:
This article is published in Linear Algebra and its Applications.The article was published on 2007-07-01 and is currently open access. It has received 43 citations till now. The article focuses on the topics: Logarithmically convex function & Convex analysis.read more
Citations
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Journal ArticleDOI
Operator log-convex functions and operator means
Tsuyoshi Ando,Fumio Hiai +1 more
TL;DR: In this paper, it was shown that a continuous nonnegative function is operator log-convex if and only if it is operator monotone decreasing and several equivalent conditions related to operator means are given for such functions.
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Operator log-convex functions and operator means
Tsuyoshi Ando,Fumio Hiai +1 more
TL;DR: In this paper, it was shown that a continuous nonnegative function on (0, ∞) is operator log-convex if and only if it is operator monotone decreasing.
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The matrix arithmetic-geometric mean inequality revisited
Rajendra Bhatia,Fuad Kittaneh +1 more
TL;DR: In this article, ideas related to matrix versions of the arithmetic-geometric mean inequality are explained, and a matrix version of the mean inequality can be found in the present paper.
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A matrix subadditivity inequality for f(A + B) and f(A) + f(B)
TL;DR: In this paper, Ando and Zhan proved a subadditivity inequality for concave functions for all symmetric norms (in particular for all Schatten p-norms).
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Norm and anti-norm inequalities for positive semi-definite matrices
TL;DR: In this paper, a class of functionals containing the Schatten q-norms for q ∈ (0, 1) and q < 0 were investigated, and some subadditivity results involving symmetric (unitarily invariant) norms were obtained.
References
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Book
Topics in Matrix Analysis
TL;DR: The field of values as discussed by the authors is a generalization of the field of value of matrices and functions, and it includes singular value inequalities, matrix equations and Kronecker products, and Hadamard products.
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On the singular values of a product of operators
Rajendra Bhatia,Fuad Kittaneh +1 more
TL;DR: For compact Hilbert space operators A and B, the singular values of B and A were shown to be dominated by the singular value of 1/2/1/2 (AA + BB + BB ) as mentioned in this paper.