Operator norms and lower bounds of generalized hausdorff matrices

Chang Pao Chena*, Kuo-Zhong Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Let A(an,k)n,k≥0 be a non-negative matrix. Denote by Lp,q(A) the supremum of those L satisfying the following inequality: The purpose of this article is to establish a Bennett-type formula for {pipe}{pipe}H0{pipe}{pipe}p, p and a Hardy-type formula for Lp, p(Hαμ) and Lp, p(Hαμ), where Hαμ is a generalized Hausdorff matrix and 0<p≤1. Similar results are also established for Lp, p(Hαμ) and Lp, p((Hαμ)t) for other ranges of p and q. Our results extend [Chen and Wang, Lower bounds of Copson type for Hausdorff matrices, Linear Algebra Appl. 422 (2007), pp. 208-217] and [Chen and Wang, Lower bounds of Copson type for Hausdorff matrices: II, Linear Algebra Appl. 422 (2007) pp. 563-573] from H0μ to Hαμ with α ≥ 0 and completely solve the value problem of {pipe}{pipe}H0{pipe}{pipe}p, p, Lp, p Hαμ, Lp, p Hαμ, and Lp, p ((Hαμ)t) for αNU{0}.

Original languageEnglish
Pages (from-to)321-337
Number of pages17
JournalLinear and Multilinear Algebra
Volume59
Issue number3
DOIs
StatePublished - 1 Mar 2011

Keywords

  • Generalized hausdorff matrices
  • Lower bound
  • Operator norms

Fingerprint Dive into the research topics of 'Operator norms and lower bounds of generalized hausdorff matrices'. Together they form a unique fingerprint.

Cite this