Mualla Birgül HUBAN, Hamdullah BAŞARAN, Mehmet GÜRDAL

Artan Operatör Konveks Fonksiyon İçin Berezin Sayı Eşitsizliği

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.

Anahtar Kelimeler:

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

Berezin Number Inequality for Increasing Operator Convex Function

Keywords:

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

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