STATISTICAL CONVERGENCE AND SOME QUESTIONS OF OPERATOR THEORY

GÜRDAL M. , YAMANCI U.

DYNAMIC SYSTEMS AND APPLICATIONS, vol.24, no.3, pp.305-311, 2015 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 3
  • Publication Date: 2015
  • Title of Journal : DYNAMIC SYSTEMS AND APPLICATIONS
  • Page Numbers: pp.305-311
  • Keywords: Statistical convergence, Compact operator, Schatten-Neumann class, Berezin symbol, REPRODUCING KERNELS, BEREZIN SYMBOLS

Abstract

We use the concepts of statistical convergence and Berezin symbols for solving of some problems of operator theory. Namely, we prove that under some conditions the weak statistical limit of compact operators is compact. We also use statistical convergence for the solving of similar problem for the sequence of operators from Schatten-Neuman class. Some related questions are also discussed.