Infinite matrices bounded on weighted ℓ1 spaces

Joseph J. Williams, Qiang Ye

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

This paper investigates conditions under which an infinite matrix will be bounded as a linear operator between two weighted ℓ1 spaces, and examines the relationship between the matrix and the weight vectors. It is shown that every infinite matrix is bounded as an operator between two weighted ℓ1 spaces, for suitable weights. Necessary conditions and separate sufficient conditions for an infinite matrix to be bounded on some weighted ℓ1 space (with the same weight for its domain and range) are given. We then show a connection between these results and the classical Schur Test which gives a sufficient condition for an infinite matrix to be bounded on the standard ℓ2 (Hilbert) space.

Original languageEnglish
Pages (from-to)4689-4700
Number of pages12
JournalLinear Algebra and Its Applications
Volume438
Issue number12
DOIs
StatePublished - Jun 15 2013

Bibliographical note

Funding Information:
Corresponding author. E-mail addresses: Joseph_Williams@umanitoba.ca (J.J. Williams), qiang.ye@uky.edu (Q. Ye). 1 Research of this author was supported in part by NSF under Grant DMS-0915062.

Keywords

  • Infinite matrix
  • Matrix norm
  • Weighted sequence space
  • ℓ Space
  • ℓ Space

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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