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

  • Nəşrin Növü: Article / Article
  • Cild: 17 Say: 2
  • Nəşr tarixi: 2023
  • Doi nömrəsi: 10.7153/oam-2023-17-31
  • jurnalın adı: OPERATORS AND MATRICES
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Səhifə sayı: pp.469-484
  • Adres: Bəli

Qısa məlumat

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.