Some Convergence Theorems for Operator Sequences


Mustafayev H.

INTEGRAL EQUATIONS AND OPERATOR THEORY, vol.92, no.4, 2020 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 92 Issue: 4
  • Publication Date: 2020
  • Doi Number: 10.1007/s00020-020-02591-8
  • Journal Name: INTEGRAL EQUATIONS AND OPERATOR THEORY
  • Journal Indexes: Science Citation Index Expanded, Scopus, MathSciNet, zbMATH
  • Keywords: Hilbert space, Banach space, Compact operator, Toeplitz operator, Composition operator, Model operator, Local spectrum, Operator sequence, Operator average, Convergence

Abstract

Let A, T, and B be bounded linear operators on a Banach space. This paper is concerned mainly with finding some necessary and sufficient conditions for convergence in operator norm of the sequences {A(n)TB(n)} and {1/n Sigma(n-1)(i=0) A(i)TB(i)}. These results are applied to the Toeplitz, composition, and model operators. Some related problems are also discussed.