Related papers: Numerical radius in Hilbert $C^*$-modules
In this paper, we present several new bounds for the norm and numerical radius of sums of Hilbert space operators. The obtained bounds form a new collection that enriches our understanding of these bounds. We compare our bounds with the…
We provide the definition and fundamental properties of algebraic elements with respect to an operator satisfying hypothesis (h). Furthermore, we analyze Hilbert modules using C_0-operators relative to a bounded finitely connected region…
In this article, we prove an inner product inequality for Hilbert space operators. This inequality, then, is utilized to present a general numerical radius inequality using convex functions. Applications of the new results include obtaining…
Let $\Omega\subset\mathbb{R}^n$, $n\ge 2$, be a bounded connected $C^2$ domain. For any unit vector $\nu\in\mathbb{R}^n$, let $T_{\lambda}^{\nu}=\{x\in\mathbb{R}^n:x\cdot\nu=\lambda\}$,…
Let $A$ be a positive bounded linear operator acting on a complex Hilbert space $\big(\mathcal{H}, \langle \cdot\mid \cdot\rangle \big)$. Let $\omega_A(T)$ and ${\|T\|}_A$ denote the $A$-numerical radius and the $A$-operator seminorm of an…
Consider a complex Hilbert space $\left(\mathcal{H}, \langle \cdot, \cdot \rangle\right)$ equipped with a positive bounded linear operator $A$ on $\mathcal{H}$. This induces a semi-norm $\|\cdot\|_A$ through the semi-inner product $\langle…
The radius of comparison is an invariant for unital C*-algebras which extends the theory of covering dimension to noncommutative spaces. We extend its definition to general C*-algebras, and give an algebraic (as opposed to…
Operator matrices have played a significant role in studying Hilbert space operators. In this paper, we discuss further properties of operator matrices and present new estimates for the operator norms and numerical radii of such operators.…
Let $\big(\mathcal{H}, \langle \cdot\mid \cdot\rangle \big)$ be a complex Hilbert space and $A$ be a positive (semidefinite) bounded linear operator on $\mathcal{H}$. The semi-inner product induced by $A$ is given by ${\langle x\mid…
We introduce the notion of approximate numerical radius (Birkhoff) orthogonality and investigate its significant properties. Let $T, S\in \mathbb{B}(\mathscr{H})$ and $\varepsilon \in [0, 1)$. We say that $T$ is approximate numerical radius…
Consider $\mathcal{H}$ is a complex Hilbert space and $A$ is a positive operator on $\mathcal{H}.$ The mapping $\langle\cdot,\cdot\rangle_A: \mathcal{H}\times \mathcal{H} \to \mathbb {C}$, defined as $\left\langle…
Several new improvements of the $A$-numerical radius inequalities for operators acting on a semi-Hilbert space, i.e., a space generated by a positive operator $A$, are proved. In particular, among other inequalities, we show that…
Let $\mathcal{A}$ be a unital $\mathbf{C}^*$-algebra with unit $e$. We develop several inequalities for a positive linear functional $f$ on $\mathcal{A}$ and obtain several bounds for the numerical radius $v(a)$ of an element $a\in…
Some new inequalities for the norm and the numerical radius of composite operators generated by a pair of operators are given.
This article implements a simple convex approach and block techniques to obtain several new refined versions of numerical radius inequalities for Hilbert space operators. This includes comparisons among the norms of the operators, their…
In the first part of the paper, we use states on $C^*$-algebras in order to establish some equivalent statements to equality in the triangle inequality, as well as to the parallelogram identity for elements of a pre-Hilbert $C^*$-module. We…
The weighted numerical radius of a Hilbert space operator has been defined recently. This article explores other properties and uses this newly defined numerical radius to obtain several new interesting inequalities for the weighted…
Let $A$ be a bounded linear operator on a complex Hilbert space and $\Re(A)$ ( $\Im(A)$ ) denote the real part (imaginary part) of A. Among other refinements of the lower bounds for the numerical radius of $A$, we prove that…
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 $T,S\in \mathbb{B}(\mathscr{H})$…
Let $A$ be a positive (semidefinite) bounded linear operator acting on a complex Hilbert space $\big(\mathcal{H}, \langle \cdot\mid \cdot\rangle \big)$. The semi-inner product ${\langle x\mid y\rangle}_A := \langle Ax\mid y\rangle$, $x,…