Related papers: Improvement of numerical radius inequalities

Let $\mathcal{H}$ be a complex Hilbert space and let $\big\{A_{n}\big\}_{n\geq 1}$ be a sequence of bounded linear operators on $\mathcal{H}$. Then a bounded operator $B$ on a Hilbert space $\mathcal{K} \supseteq \mathcal{H}$ is said to be…

We investigate some aspects of various numerical radius orthogonalities and numerical radius parallelism for bounded linear operators on a Hilbert space $\mathscr{H}$. Among several results, we show that if $T,S\in \mathbb{B}(\mathscr{H})$…

In 1992, Szyld provided a sequence of lower bounds for the spectral radius of a nonnegative matrix $A$, based on the geometric symmetrization of powers of $A$. In 1998, Ta\c{s}\c{c}i and Kirkland proved a companion result by giving a…

We present several operator and norm inequalities for Hilbert space operators. In particular, we prove that if $A_{1},A_{2},...,A_{n}\in {\mathbb B}({\mathscr H})$, then…

We define a function on the $C^{\ast}$-algebra of all bounded linear Hilbert space operators, which generalizes the operator radii, and we present some basic properties of this function. Our results extend several results in the literature.

Let $\mathcal{B}(\mathcal{H})$ be the algebra of all bounded linear operators on a complex Hilbert space $\mathcal{H}$. In this paper, we first establish several sharp improved and refined versions of the Bohr's inequality for the functions…

In this paper, we prove the relation $\frac{r_{A}(T) + r_{A}(T^{\diamond}) + |r_{A}(T^{\diamond}) - r_{A}(T)|}{2} = \sup \{ |\lambda|: \lambda \in \sigma_{A}(T)\}$, where $A$ is a positive semidefinite operator (not necessarily to have a…

The primary purpose of this paper is to show the existence of normal square and nth roots of some classes of bounded operators on Hilbert spaces. Two interesting simple results hold. Namely, under simple conditions we show that if any…

Suppose $L(H)$ is the space of all bounded linear operators on a complex Hilbert space $H.$ This article deals with the problem of characterizing the extreme contractions of $L(H)$ with respect to the numerical radius norm on $L(H).$ In…

Let $A$ be a positive definite operator on a Hilbert space $H$, and $|||.|||$ be a unitarily invariant norm on $B(H)$. We show that if $f$ is an operator monotone function on $(0,\infty)$ and $n\in \mathbb{N}$, then $|||D^n…

Consider a solution $f\in C^{2}(\Omega)$ of a prescribed mean curvature equation \[ {\rm div}\left(\frac{\nabla f}{\sqrt{1+|\nabla f|^{2}}}\right)=2H(x,f) \ \ \ \ {\rm in} \ \ \Omega, \] where $\Omega\subset \Real^{2}$ is a domain whose…

The numerical radius of a matrix is a scalar quantity that has many applications in the study of matrix analysis. Due to the difficulty in computing the numerical radius, inequalities bounding it have received a considerable attention in…

We study different operator radii of homomorphisms from an operator algebra into $B(H)$ and show that these can be computed explicitly in terms of the usual norm. As an application, we show that if $\Omega$ is a $K$-spectral set for a…

It has been recently shown that $|| F_n(A) ||\leq 2$, where $A$ is a linear continuous operator acting in a Hilbert space, and $F_n$ is the Faber polynomial of degree $n$ corresponding to some convex compact $E\subset \mathbb C$ containing…

In this paper, we improve and generalize the operator versions of Kantorovich and Wielandt inequalities for positive linear maps on Hilbert space. Our results are more extensive and precise than many previous results due to Fu and He…

We present some reverse Young-type inequalities for the Hilbert-Schmidt norm as well as any unitarily invariant norm. Furthermore, we give some inequalities dealing with operator means. More precisely, we show that if $A, B\in {\mathfrak…

Let $H$ be a complex separable Hilbert space and $B(H)$ the algebra of all bounded linear operators on $H$. In this paper, we give considerable generalizations of the inequalities for norms of commutators of normal operators. Let $S, T \in…

We present several sharp upper bounds and some extension for product operators. Among other inequalities, it is shown that if , , are non-negative continuous functions on such that , , then for all non-negative operator monotone decreasing…

This article has two interpenetrating motifs. One is an exposition of some major ideas and techniques behind the use of block matrices, and especially their positivity properties. This is done by focussing on one major problem:…

In this paper, several refinements of the Berezin number inequalities are obtained. We generalize inequalities involving powers of the Berezin number for product of two operators acting on a reproducing kernel Hilbert space $\mathcal…