Related papers: Numerical radius in Hilbert $C^*$-modules
In this paper, we investigate the generalized numerical radius $\omega_N$, associated with a matrix norm $N$ defined by $\omega_N(X) = \sup_{\theta \in \mathbb{R}} N(\operatorname{Re}(e^{i\theta}X))$. We focus on matrices whose numerical…
In a recent work of the authors, we showed some general inequalities governing numerical radius inequalities using convex functions. In this article, we present results that complement the aforementioned inequalities. In particular, the new…
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 observe that the classical notion of numerical radius gives rise to a notion of smoothness in the space of bounded linear operators on certain Banach spaces, whenever the numerical radius is a norm. We demonstrate an important class of…
Let $X$ be a compact metric space, let $A$ be a unital AH algebra with large matrix sizes, and let $B$ be a stably finite unital C*-algebra. Then we give a lower bound for the radius of comparison of $C(X) \otimes B$ and prove that the…
We present some upper and lower bounds for the numerical radius of a bounded linear operator defined on complex Hilbert space, which improves on the existing upper and lower bounds. We also present an upper bound for the spectral radius of…
If $A,B$ are bounded linear operators on a complex Hilbert space, then % $w(A) \leq \frac{1}{2}\left( \|A\|+\sqrt{r\left(|A||A^*|\right)}\right)$ and $w(AB \pm BA)\leq 2\sqrt{2}\|B\|\sqrt{ w^2(A)-\frac{c^2(\Re (A))+c^2(\Im (A))}{2} },$…
In this paper, we establish some upper bounds for numerical radius inequalities including of $2\times 2$ operator matrices and their off-diagonal parts. Among other inequalities, it is shown that if $T=\left[\begin{array}{cc} 0&X, Y&0…
In this article, we obtain several new weighted bounds for the numerical radius of a Hilbert space operator. The significance of the obtained results is the way they generalize many existing results in the literature; where certain values…
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 and improve the earlier related ones. Among other…
We present sharp lower bounds for the A-numerical radius of semi-Hilbertian space operators. We also present an upper bound. Further we compute new upper bounds for the $B$-numerical radius of $2 \times 2$ operator matrices where $B =…
It is known that, if $\Omega$ $\subset$ C is a convex set containing the numerical range of an operator A, then $\Omega$ is a C $\Omega$ -spectral set for A with C $\Omega$ $\le$ 1+ $\sqrt$ 2. We improve this estimate in unbounded cases.
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 operator on a complex Hilbert space, then $$…
Utilizing the Birkhoff--James orthogonality, we present some characterizations of the norm-parallelism for elements of $\mathbb{B}(\mathscr{H})$ defined on a finite dimensional Hilbert space, elements of a Hilbert $C^*$-module over the…
Let $\Omega$ be a symmetric cone. In this note, we introduce the Hilbert projective metric on $\Omega$ in terms of Jordan algebras and we apply it to prove that given a linear transformation $g$ such that $g(\Omega)\subset \Omega$ and a…
For a unital $C^*$-algebra $\mathcal A$ and a subspace $\mathcal B$ of $\mathcal A$, a characterization for a best approximation to an element of $\mathcal A$ in $\mathcal B$ is obtained. As an application, a formula for the distance of an…
We consider several natural ways of expressing the idea that a one-sided ideal in a C*-algebra (or a submodule in a Hilbert C*-module) is large, and show that they differ, unlike the case of two-sided ideals in C*-algebras. We then show how…
In this paper, we achieve new and improved numerical radius inequalities of operators defined on a Hilbert space by using Orlicz function and Hermite-Hadamard inequality. The upper bounds of various inequalities involving numerical radii…
Some elementary inequalities providing upper bounds for the difference of the norm and the numerical radius of a bounded linear operator on Hilbert spaces under appropriate conditions are given.
In this paper, more inequalities between the operator norm and its numerical radius, for the class of normal operators, are established. Some of the obtained results are based on recent reverse results for the Schwarz inequality in Hilbert…