Artan Operatör Konveks Fonksiyon İçin Berezin Sayı Eşitsizliği

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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