Results 21 to 30 of about 4,765 (143)
Generalized Induced Norms [PDF]
, 2004 Let ||.|| be a norm on the algebra M_n of all n-by-n matrices over the complex field C. An interesting problem in matrix theory is that "are there two norms ||.||_1 and ||.||_2 on C^n such that ||A||=max{||Ax||_2: ||x||_1=1} for all A in M_n.
C.-K. Li +7 more
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Monotonicity of unitarily invariant norms
Linear Algebra and its Applications, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Xue-Feng, Li, Ren-Cang
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Catalytic majorization and $\ell_p$ norms [PDF]
, 2007 An important problem in quantum information theory is the mathematical characterization of the phenomenon of quantum catalysis: when can the surrounding entanglement be used to perform transformations of a jointly held quantum state under LOCC (local ...
Aubrun, Guillaume, Nechita, Ion
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A class of unitarily invariant norms on 𝐵(𝐻) [PDF]
Proceedings of the American Mathematical Society, 2000 Let H H be a complex Hilbert space and let B ( H ) B(H) be the algebra of all bounded linear operators on H H . For c = ( c 1 , … , c k
Chan, JT, Tu, CCN, Li, CK
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Submultiplicativity vs subadditivity for unitarily invariant norms
Linear Algebra and its Applications, 2004 The authors prove that if \(A\) and \(B\) are two \(n\)-by-\(n\) nonzero positive semidefinite matrices and \(\|\cdot\|\) is a unitarily invariant norm on matrices satisfying \(\|\text{diag}(1,0,\dots, 0)\|\geq 1\), then the inequalities \[ {\| AB\|\over\| A\|\,\| B\|}\leq {\| A+ B\|\over\| A\|+\| B\|}\quad\text{and}\quad {\| A\circ B\|\over \| A\|\,\|
Hiai, Fumio, Zhan, Xingzhi
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Operator Monotone Functions and Convexity of Its Derivatives Norms
پژوهشهای ریاضی, 2021 Introduction Given the important role convex and quasi-convex functions play in many areas of mathematics and especially in optimization, one of the inequalities that has attracted the attention of many mathematicians in recent decades is Hermit ...
Zahra Rahimi Chegeni +2 more
doaj
Unitarily invariant norm inequalities for operators
Journal of the Egyptian Mathematical Society, 2012 10 pages, Accepted ...
Erfanian Omidvar, M. +2 more
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Norm inequalities related to the Heron and Heinz means [PDF]
, 2017 In this article, we present several inequalities treating operator means and the Cauchy-Schwarz inequality. In particular, we present some new comparisons between operator Heron and Heinz means, several generalizations of the difference version of the ...
Conde, C. +4 more
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Volume ratio, sparsity, and minimaxity under unitarily invariant norms [PDF]
2013 IEEE International Symposium on Information Theory, 2013 The current paper presents a novel machinery for studying non-asymptotic minimax estimation of high-dimensional matrices, which yields tight minimax rates for a large collection of loss functions in a variety of problems. Based on the convex geometry of finite-dimensional Banach spaces, we first develop a volume ratio approach for determining minimax ...
Ma, Zongming, Wu, Yihong
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On the separability of unitarily invariant random quantum states - the unbalanced regime
, 2018 We study entanglement-related properties of random quantum states which are unitarily invariant, in the sense that their distribution is left unchanged by conjugation with arbitrary unitary operators.
Nechita, Ion
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