Artan Operatör Konveks Fonksiyon İçin Berezin Sayı Eşitsizliği

Year 2021, Volume: 9 Issue: 6 - ICAIAME 2021, 1 - 14, 31.12.2021

Mualla Birgül Huban , Hamdullah Başaran Mehmet Gürdal

https://doi.org/10.29130/dubited.1013082

Cited By: 6

Abstract

Normalleştirilmiş $K_{\lambda}:=\frac{k_{\lambda}}{\left\Vert k_{\lambda}\right\Vert_{\mathcal{H}}}$, üretici çekirdekli $\mathcal{H}\left( \Omega\right) $, Hilbert uzayı üzerinde $A$ sınırlı lineer operatör için Berezin sembolü ve Berezin sayısı sırasıyla $A\left( \lambda\right) :=\left\langle AK_{\lambda},K_{\lambda}\right\rangle _{\mathcal{H}}$ ve $\mathrm{ber}(A):=\sup_{\lambda\in\Omega}\left\vert A{(\lambda)}\right\vert $ biçiminde tanımlanır. Bu karakteristik arasındaki durumlardan $\mathrm{ber}\left( A\right) \leq\frac{1}{\sqrt{2}}\mathrm{ber}\left(\left\vert A\right\vert +i\left\vert A^{\ast}\right\vert \right) $ eşitsizliği elde edilmiştir. Bu çalışmamızda ise onlar arasındaki diğer eşitsizlikler ispatlanmış ve Berezin sayı eşitsizlikleri için operatör konveks fonksiyonlarının bazı uygulamaları verilmiştir.

Keywords

Üretici çekirdekli Hilbert uzayı, Berezin sembolü, Berezin sayısı, Hermite-Hadamard eşitsizliği, Operatör konveksliği

Berezin Number Inequality for Increasing Operator Convex Function

Abstract

Keywords

Reproducing kernel Hilbert space, Berezin symbol, Berezin number, Hermite-Hadamard inequality, Operator convexity

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