Improved Berezin radius inequalities for functional Hilbert space operators

Authors

MOJTABA BAKHERADFollow
ULAŞ YAMANCIFollow
MOHAMMAD W. ALOMARIFollow

Correction Statement

This article has been revised, and a Corrigendum has been issued to address errors in the original manuscript. For details, please refer to the published Corrigendum.

Author ORCID Identifier

MOJTABA BAKHERAD: 0000-0003-0323-6310

ULAŞ YAMANCI: 0000-0002-4709-0993

MOHAMMAD W. ALOMARI: 0000-0002-6696-9119

Abstract

The Berezin number of an operator S is defined by ber(S) = sup_λ∈Θ |Ŝ(λ)| = sup_λ∈Θ |⟨Sĸ̂_λ, ĸ̂_λ⟩|, where Ŝ(λ) = ⟨Sĸ̂_λ, ĸ̂_λ⟩ (λ ∈ Θ) is the Berezin transform of an operator S on the functional Hilbert space ℋ = ℋ(Θ) and ĸ̂_λ = ĸ_λ / ‖ĸ_λ‖ is the normalized reproducing kernel of ℋ. In this paper, we show an improvement of the classical Cauchy–Schwarz inequality involving the Berezin number. Moreover, some Berezin numbers inequalities are proven for invertible operators.

DOI

10.55730/1300-0098.3607

Keywords

Berezin number, berezin symbol, furuta's inequality

First Page

545

Last Page

561

Publisher

The Scientific and Technological Research Council of Türkiye (TÜBİTAK)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Recommended Citation

BAKHERAD, M, YAMANCI, U, & ALOMARI, M (2025). Improved Berezin radius inequalities for functional Hilbert space operators. Turkish Journal of Mathematics 49 (5): 545-561. https://doi.org/10.55730/1300-0098.3607