Lower bounds of Copson type for Hausdorff matrices
type: Item
instance of: scholarly article
title: Lower bounds of Copson type for Hausdorff matrices
zbMATH Open document ID: 1117.15019
author: Chang-Pao Chen
author: Kuo-Zhong Wang
published in: Linear Algebra and its Applications
publication date: 2007-02-14T00:00:00Z
review text: Let \(A=\left( a_{m,n}\right) _{m,n\geq 0}\) be a nonnegative matrix. For \( 1\leq p\leq \infty \) and \(0<q\leq p\) let \(L_{p,q}(A)\) be the supremum of the numbers \(L\) satisfying the inequality: \[ \left( \sum_{m=0}^{\infty }\left( \sum_{n=0}^{\infty }a_{m,n}x_{n}\right) ^{q}\right) ^{1/q}\geq L\left( \sum_{n=0}^{\infty }x_{n}^{p}\right) ^{1/p}, \] whenever \(\left\{ x_{n}\right\} _{n=0}^{\infty }\in \ell ^{p}\) with \( x_{n}\geq 0\) for all \(n\geq 0\). The authors give the exact value of \( L_{p,q}(A)\) in the case when \(A\) is a Hausdorff matrix. Applications to Cesàro matrices, Hölder matrics, gamma matrices, and generalized Euler matrices are given.
reviewed by: Omar Hirzallah
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 40G05
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 5126063
zbMATH Keywords: lower bound
zbMATH Keywords: Cesàro matrices
zbMATH Keywords: Hölder matrices
zbMATH Keywords: gamma matrices
zbMATH Keywords: generalized Euler matrices
zbMATH Keywords: matrix inequality
zbMATH Keywords: nonnegative matrix
MaRDI profile type: Publication
full work available at URL: j.laa.2006.07.005
OpenAlex ID: W2086296002
cites work: Lower bounds for matrices
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DOI: 10.1016/J.LAA.2006.07.005
description: scientific article; zbMATH DE number 5126063