Specht Oranına Göre Berezin Sayı Eşitsizlikleri

Year 2022, Volume: 9 Issue: 4, 1201 - 1214, 31.12.2022

Mehmet Gürdal Hamdullah Başaran

https://doi.org/10.31202/ecjse.1131830

Abstract

Berezin dönüşümü, düzgün fonksiyonları, analitik fonksiyonların Hilbert uzayları üzerindeki operatörlerle ilişkilendirir. Hilbert fonksiyonel uzay H(Ω) üzerinde bir A operatörünün Berezin sembolü ve Berezin sayısı
A ̃(μ)=〈A K_μ/K_μ ,K_μ/K_μ 〉,μ∈Ω ve ber(A)=sup┬(μ∈Ω)⁡|A ̃(μ)|
şeklinde tanımlanır. Bu A ̃ sınırlı fonksiyonu kullanılarak Hilbert fonksiyonel uzay operatörlerinin bazı yeni Berezin sayı eşitsizliklerini sunulmuştur. Specht oranı yardımıyla bazı eşitsizlikler genelleştirilmiş ve iyileştirilmiştir. Aynı zamanda bu iyileştirmeler kullanılarak Berezin yarıçap ve Berezin norm için çeşitli yeni eşitsizlikler gösterilmiştir.

Keywords

Berezin sayısı, Hilbert fonksiyonel uzay, Specht oranı, pozitif operatör

Berezin number inequalities in terms of Specht's

Abstract

Smooth functions are associated with operators on Hilbert spaces of analytic functions through the Berezin transform. The Berezin symbol and the Berezin number of an operator A on the Hilbert functional space H(Ω) over some set Ω with the reproducing kernel are defined, respectively, by
A ̃(μ)=〈A K_μ/K_μ ,K_μ/K_μ 〉,μ∈Ω and ber(A)=sup┬(μ∈Ω)⁡|A ̃(μ)|.
By using this bounded function A ̃, we present some new Berezin number inequalities of Hilbert functional space operators. Some inequalities with respect to Specht's ratio are improved and generalized. Using these modifications, we also establish various new inequalities for the Berezin radius and Berezin norm of operators.

Keywords

Berezin number, Hilbert functional space, Specht, positive operator

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