THE WEIGHTED AND THE DAVIS-WIELANDT BEREZIN NUMBER

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Garayev M. U. B. A. R. I. Z., Bakherad M. O. J. T. A. B. A., Tapdigoglu R. A. M. I. Z.

OPERATORS AND MATRICES, vol.17, no.2, pp.469-484, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.7153/oam-2023-17-31
  • Journal Name: OPERATORS AND MATRICES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.469-484
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

A functional Hilbert space is the Hilbert space of complex-valued functions on some set Theta subset of C that the evaluation functionals phi(lambda) (f) = f (lambda), lambda is an element of Theta are continuous onH. The Berezin number of an operator T is defined by ber(T) = sup vertical bar(T) over tilde (lambda)vertical bar = sup vertical bar < T (K) over cap (lambda),(K) over cap (lambda) >vertical bar, the operator T acts on the reproducing kernel Hilbert space H =H(Theta) over some (non-empty) set Theta. In this paper, we defined the weighted Berezin radius and the weighted Berezin norms and then we obtain some related inequalities. It is shown, among other inequalities, that if T is an element of L(H) and t is an element of[0,1], then ber(t)(2) (T ) <= (1 - 2t + 2t(2))parallel to T T* + T*T parallel to(ber,1) + (1 - 2t)ber T-2 + T-*2). Moreover, we generalize the Davis-Wielandt Berezin number and present some inequalities in-volving this definition.