Results 91 to 100 of about 581 (209)
Hölder-type norm inequalities for schur products of matrices
, 1987 For a unitarily invariant norm ∥·∥φon Mn and p ⩾ 1 we define ∥Aφ, p, by ∥∣A∣p∥1pφ. Then ∥·∥φ, p is again a unitarily invariant norm. We give Hölder-type inequalities for Schur products of the form ∥A∘B∥φ0,p0⩽∥A∥φ1,p1·∥B∥φ2,p2.. As a corollary, we settle,
Okubo, K.
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Singular value inequalities of matrices via increasing functions
Journal of Inequalities and ApplicationsLet A, B, X, and Y be n × n $n\times n$ complex matrices such that A is self-adjoint, B ≥ 0 $B\geq 0$ , ± A ≤ B $\pm A\leq B$ , max ( ∥ X ∥ 2 , ∥ Y ∥ 2 ) ≤ 1 $\max ( \Vert X \Vert ^{2}, \Vert Y \Vert ^{2} ) \leq 1$ , and let f be a nonnegative increasing
Wasim Audeh +3 more
doaj +1 more source
Norms on complex matrices induced by random vectors II: extension of weakly unitarily invariant norms [PDF]
, 2023 Ángel Chávez +2 more
openalex +1 more source
A note on the magnetic Steklov operator on functions
Mathematika, Volume 71, Issue 4, October 2025.Abstract We consider the magnetic Steklov eigenvalue problem on compact Riemannian manifolds with boundary for generic magnetic potentials and establish various results concerning the spectrum. We provide equivalent characterizations of magnetic Steklov operators which are unitarily equivalent to the classical Steklov operator and study bounds for the ...
Tirumala Chakradhar +3 more
wiley +1 more source
On the perturbation bound in unitarily invariant norms for subunitary polar factors
, 2008 Let Crm×n be the set of m×n complex matrices with rank r, and let A∈Crm×n and A∼=A+E∈Crm×n have the generalized polar decompositionsA=QHandA∼=Q∼H∼.In this article, a new perturbation bound for subunitary polar factors in any unitarily invariant norm is ...
Li, Wen
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The stability of the unit balls of symmetric and unitarily invariant norms
, 1997 A compact convex set K is called stable if the midpoint mapping, K × K → K, (x, y) → (x + y)2, is open. The main result asserts that the stability of the closed unit ball of a unitarily invariant norm is equivalent to the stability of the closed unit ...
de Sá, Eduardo Marques
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Normal operators and inequalities in norm ideals
, 2009 In this work we characterize normal invertible operators via inequalities with unitarily invariant norm of elementary ...
Conde, Cristian Marcelo, Conde, Cristian
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The convex analysis of unitarily invariant matrix functions
, 1995 A fundamental result of von Neumann's identies unitarily invariant matrix norms as symmetric gauge functions of the singular values. Identifying the subdierential of such a norm is important in matrix approximation algorithms, and in studying the ...
A. S. Lewis
core
Norm inequalities in operator ideals [PDF]
, 2008 In this paper we introduce a new technique for proving norm inequalities in operator ideals with a unitarily invariant norm. Among the well-known inequalities which can be proved with this technique are the Löwner–Heinz inequality, inequalities relating ...
Larotonda, Gabriel +1 more
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A norm inequality for pairs of commuting positive semidefinite matrices [PDF]
, 2015 For $k=1,\ldots,K$, let $A_k$ and $B_k$ be positive semidefinite matrices such that, for each $k$, $A_k$ commutes with $B_k$. We show that, for any unitarily invariant norm, \[ |||\sum_{k=1}^K A_kB_k||| \le ||| (\sum_{k=1}^K A_k)\;(\sum_{k=1}^K B_k)|||. \
Koenraad Mr Audenaert +5 more
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