Lower bounds of Copson type for weighted mean matrices and Nörlund matrices

Chang Pao Chen*, Kuo-Zhong Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Let 1 ≤ p ≤ ∞, 0 < q ≤ p, and A = (an,k)n,k≥0 ≥ 0. Denote by Lp,q(A) the supremum of those L satisfying the following inequality: whenever and X ≥ 0. In this article, the value distribution of Lp,q(A) is determined for weighted mean matrices, Norlund matrices and their transposes. We express the exact value of Lp,q(A) in terms of the associated weight sequence. For Norlund matrices and some kinds of transposes, this reduces to a quotient of the norms of such a weight sequence. Our results generalize the work of Bennett.

Original languageEnglish
Pages (from-to)343-353
Number of pages11
JournalLinear and Multilinear Algebra
Volume58
Issue number3
DOIs
StatePublished - 1 Apr 2010

Keywords

  • Lower bound
  • Norlund matrices
  • Weighted mean matrices

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