Equivalence constants for matrix norms: A problem of Goldberg
type: Item
instance of: scholarly article
title: Equivalence constants for matrix norms: A problem of Goldberg
zbMATH Open document ID: 0956.15013
DOI: 10.1016/S0024-3795(99)00155-X
author: Yanyan Li
published in: Linear Algebra and its Applications
publication date: 2001-03-02T00:00:00Z
review text: The equivalence constants for the \(\ell^p\)-coefficient norms and \(\ell^q\)-operator norms \((1\leqslant p,q\leqslant\infty)\) of complex \(n\times m\) matrices are studied. The author establishes some new inequalities and provides a variety of known results for Goldberg's problem: Determine the best (least) constant \(c=c(m,n,p,q)\) such that \(|A|_p\leqslant c\|A\|_q\) for all \(m\times n\) matrices~\(A\). Here \(\|\cdot\|_p\) stands for the \(\ell^p\)-coefficient norm, and \(\|\cdot\|_q\) stands for the \(\ell^q\)-operator norm.
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 15A45
zbMATH DE Number: 1421380
zbMATH Keywords: matrix norm
zbMATH Keywords: complex matrices
zbMATH Keywords: Goldberg's problem
zbMATH Keywords: \(\ell^p\)-coefficient norm
zbMATH Keywords: \(\ell^q\)-operator norm
reviewed by: A. R. Alimov
MaRDI profile type: Publication
cites work: Schur multipliers
cites work: Q4112938
cites work: Q4850055
cites work: Q4039882
cites work: Equivalence constants forlpnorms of matrices
cites work: BILINEAR FORMS BOUNDED IN SPACE [p, q]
cites work: Q5556050
cites work: Isometries for the vector (p,q) norm and the induced (p,q) norm
cites work: Norms of certain matrices with applications to variations of the spectra of matrices and matrix pencils
cites work: The Schur multiplication in tensor algebras
cites work: On a conjecture by Goldberg and Newman
full work available at URL: s0024-3795(99)00155-x
OpenAlex ID: W1990899218
Recommended article: Equivalence constants for certain matrix norms. II
Recommended article: Equivalence constants forlpnorms of matrices
Recommended article: Equivalence constants for certain matrix norms.
Recommended article: Equality cases in matrix norm inequalities of golden-thompson type
Recommended article: Q4248726
Recommended article: Generalization of Golden-Thompson type inequalities for normal matrices
Recommended article: Q3752116
Recommended article: The question of equivalence for generalized Hausdorff matrices
Recommended article: Q5371779
Recommended article: Constant norms and numerical radii of matrix powers
description: scientific article; zbMATH DE number 1421380