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 …

Let A be a bounded linear operator on a complex Hilbert space and ℜ (A)(ℑ (A)) denote the
real part (imaginary part) of A. Among other refinements of the lower bounds for the …

The aim of this paper is to provide new upper bounds of ω (T), which denotes the numerical
radius of a bounded operator T on a Hilbert space (H,〈·,·〉). We show the Aczél inequality in …

In this paper, we aim to introduce and characterize the numerical radius orthogonality of
operators on a complex Hilbert space HH which are bounded with respect to the seminorm …

New inequalities for the numerical radius of bounded linear operators defined on a complex
Hilbert space HH are given. In particular, it is established that if T is a bounded linear …

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^) …

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 …

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 …