NEW BEREZIN RADIUS UPPER BOUNDS

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GÜRDAL M., Tapdigoglu R.

PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS, vol.49, no.2, pp.210-218, 2023 (ESCI)

• Publication Type: Article / Article
• Volume: 49 Issue: 2
• Publication Date: 2023
• Doi Number: 10.30546/2409-4994.2023.49.2.210
• Journal Name: PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS
• Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
• Page Numbers: pp.210-218
• Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

In this paper, we provide the new Berezin radius inequalities on the space of operators defined on a functional Hilbert space. By using these inequalities, we obtain various upper bounds for the Berezin radius of functional Hilbert space operators. We prove, in particular, the following sharp upper bound ber(2) (S* T) <= 1/2 xi + 2 ber (S * T)parallel to vertical bar T vertical bar(2) + vertical bar S vertical bar(2) parallel to(ber) + delta/xi + 2 parallel to vertical bar T vertical bar(4) + vertical bar S vertical bar(4)parallel to(ber) for arbitrary T, S is an element of B(H) and xi >= 0. Other related issues are also discussed.