This book is a self-contained advanced monograph on inequalities involving the numerical
radius of bounded linear operators acting on complex Hilbert spaces. The study of various …

In this paper we present new upper bounds for the numerical radius of bounded linear
operators defined on a complex Hilbert space. Further we obtain estimations for upper …

We obtain new inequalities involving Berezin norm and Berezin number of bounded linear
operators defined on a reproducing kernel Hilbert space H. Among many inequalities …

In this article, we introduce the definition of the weighted numerical radius ω _ ν (T) ω ν (T) of
a Hilbert space operator T, and present. many interesting properties of this newly defined …

Let A= A ij be an n× n operator matrix, where each A ij is a bounded linear operator on a
complex Hilbert space. Among other numerical radius bounds, we show that w (A)≤ w (A^) …

Several refinements of norm and numerical radius inequalities of bounded linear operators
on a complex Hilbert space are given. In particular, we show that if A is a bounded linear …

If A, B are bounded linear operators on a complex Hilbert space, then we prove that w (A) ≤
& 1 2\left (‖ A ‖+ r\left (| A|| A^*|\right)\right),\w (AB ± BA) ≤ & 2 2 ‖ B ‖ w^ 2 (A)-c^ 2 (R …

In this paper, we provide a new norm (α-Berezin norm) on the space of all bounded linear
operators defined on a reproducing kernel Hilbert space, which generalizes the Berezin …

Using the polar decomposition of a bounded linear operator A defined on a complex Hilbert
space, we obtain several numerical radius inequalities of the operator A, which generalize …

Acta Mathematica Sinica, English Series Page 1 Acta Mathematica Sinica, English Series
Jul., 2023, Vol. 39, No. 7, pp. 1219–1228 Published online: April 15, 2023 https://doi.org/10.1007/s10114-023-2090-1 …