利用超二次函数和凸函数改进了Berezin数不等式

Pub Date : 2023-01-01 DOI:10.2298/fil2301265c

Fengsheng Chien, M. Bakherad, M. Alomari

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引用次数: 1

摘要

本文推广并改进了Hilbert空间算子的Berezin数不等式。也就是说，我们利用超二次性和凸性的概念，改进了Hermite-Hadamard不等式和其他一些最近的结果。然后我们将这些不等式推广到Berezin数。在其他不等式中，如果S T ?L(H(?))这样她(T) ?ber(|S|) f是非负超二次函数，那么f (ber (T))b (f (|S|)) ?f (||S| ?ber (T) |))。

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Refined Berezin number inequalities via superquadratic and convex functions

In this paper, we generalize and refine some Berezin number inequalities for Hilbert space operators. Namely, we refine the Hermite-Hadamard inequality and some other recent results by using the concept of superquadraticity and convexity. Then we extend these inequalities for the Berezin number. Among other inequalities, it is shown that if S, T ? L(H(?)) such that ber(T) ? ber(|S|) and f is a nonnegative superquadratic function, then f (ber (T)) ? ber(f (|S|)) ? ?ber (f (||S| ? ber (T)|)).

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