Improvements of some Berezin radius inequalities


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GÜRDAL M., Alomari M. W.

Constructive Mathematical Analysis, vol.5, no.3, pp.141-153, 2022 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 5 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.33205/cma.1110550
  • Journal Name: Constructive Mathematical Analysis
  • Journal Indexes: Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.141-153
  • Keywords: Berezin radius, Furuta inequality, Mixed Schwarz inequality
  • Süleyman Demirel University Affiliated: Yes

Abstract

© 2022 Himia, Fizika ta Tehnologia Poverhni. All rights reserved.The Berezin transform Ae and the Berezin radius of an operator A on the reproducing kernel Hilbert space over some set Qwith normalized reproducing kernel kη := kKKηηk are defined, respectively, by Ae(η) = hAkη, kηi, η ∈ Qand ber(A):= supη∈Q|||Ae(η) |||. A simple comparison of these properties produces the inequalities 14 kA∗A + AA∗k ≤ ber2 (A) ≤ 21 kA∗A + AA∗k. In this research, we investigate other inequalities that are related to them. In particular, for A ∈ L(H(Q)) we prove that ber2 (A) ≤ 12 kA∗A + AA∗kber − 14 ηinf ∈Q ((|fA|(η)) − (|gA∗|(η) ))2