Some New Applications of Berezin Symbols

Bhunia P., Garayev M. T., Paul K., Tapdigoglu R.

COMPLEX ANALYSIS AND OPERATOR THEORY, vol.17, no.6, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 6
  • Publication Date: 2023
  • Doi Number: 10.1007/s11785-023-01404-1
  • Journal Name: COMPLEX ANALYSIS AND OPERATOR THEORY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

We study some problems of operator theory by using Berezin symbols approach. Namely, we investigate in terms of Berezin symbols invariant subspaces of isometric composition operators on H (Omega). We discuss operator corona problem, in particular, the Toeplitz corona problem. Further, we characterize unitary operators in terms of Berezin symbols. We show that the well known inequality w (A) >= 1/2 parallel to A parallel to for numerical radius is not true for the Berezin number of operators, which is defined) by ber (A) := sup(lambda is an element of Omega) vertical bar(a) over tilde(lambda)vertical bar where (A) over tilde (lambda) := < A (k) over tilde (lambda,) k(lambda)> is the Berezin symbol of operator A : H (Omega) -> H (Omega). Finally, we provide a lower bound for ber (A) .