Reproducing kernels, Engliš algebras and some applications

Karaev M. T., GÜRDAL M., HUBAN M. B.

Studia Mathematica, vol.232, no.2, pp.113-141, 2016 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 232 Issue: 2
  • Publication Date: 2016
  • Doi Number: 10.4064/sm8385-4-2016
  • Journal Name: Studia Mathematica
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.113-141
  • Keywords: Berezin symbol, Hardy space, Invariant subspace, Reproducing kernel, Riccati equation, Toeplitz operator
  • Isparta University of Applied Sciences Affiliated: Yes

Abstract

We introduce the notion of Engliš algebras, defined in terms of reproducing kernels and Berezin symbols. Such algebras were apparently first investigated by Engliš (1995). Here we give some new results on Engliš C∗-algebras on abstract reproducing kernel Hilbert spaces and some applications to various questions of operator theory. In particular, we give applications to Riccati operator equations, zero Toeplitz products, and the existence of invariant subspaces for some operators.