Related papers: Spectral sets and operator radii
Let $\sigma(A)$, $\rho(A)$ and $r(A)$ denote the spectrum, spectral radius and numerical radius of a bounded linear operator $A$ on a Hilbert space $H$, respectively. We show that a linear operator $A$ satisfying $$\rho(AB)\le r(A)r(B)…
In this paper, we aim to introduce and characterize the concept of numerical radius orthogonality of operators on a complex Hilbert space $\mathcal{H}$ which are bounded with respect to the semi-norm induced by a positive operator $A$ on…
Let $\mathcal{H}$ be a complex Hilbert space and let $A$ be a positive operator on $\mathcal{H}$. We obtain new bounds for the $A$-numerical radius of operators in semi-Hilbertian space $\mathcal{B}_A(\mathcal{H})$ that generalize and…
For a given bounded positive (semidefinite) linear operator $A$ on a complex Hilbert space $\big(\mathcal{H}, \langle \cdot\mid \cdot\rangle \big)$, we consider the semi-Hilbertian space $\big(\mathcal{H}, \langle \cdot\mid \cdot\rangle_A…
Let $A$ be a positive operator on a complex Hilbert space $\mathcal{H}.$ We present inequalities concerning upper and lower bounds for $A$-numerical radius of operators, which improve on and generalize the existing ones, studied recently in…
In this paper, we aim to introduce the notion of the spectral radius of bounded linear operators acting on a complex Hilbert space $\mathcal{H}$, which are bounded with respect to the seminorm induced by a positive operator $A$ on…
This paper is a continuation of a recent work on a new norm, christened the $ (\alpha, \beta)$-norm, on the space of bounded linear operators on a Hilbert space. We obtain some upper bounds for the said norm of $n\times n$ operator…
We describe all isometries of the $q$-numerical radius on the space ${\mathcal K}(\mathcal H)$ of compact operators on a (possibly infinite-dimensional) Hilbert space $\mathcal H$.
We define the complete numerical radius norm for homomorphisms from any operator algebra into ${\mathcal B}({\mathcal H})$, and show that this norm can be computed explicitly in terms of the completely bounded norm. This is used to show…
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…
In this paper we give several expressions of spectral radius of a bounded operator on a Hilbert space, in terms of iterates of Aluthge transformation, numerical radius and the asymptotic behavior of the powers of this operator. Also we…
In this paper, we introduce a new type of parallelism for bounded linear operators on a Hilbert space $\big(\mathscr{H}, \langle \cdot ,\cdot \rangle\big)$ based on numerical radius. More precisely, we consider operators $T$ and $S$ which…
We give an alternative lower bound for the numerical radii of Hilbert space operators. As a by-product, we find conditions such that \begin{equation*} \omega\left(\left[\begin{array}{cc} 0 & R \\ S & 0 \end{array}\right]\right)=\frac{\Vert…
Let ${\mathbb B}(\mathscr H)$ denote the set of all bounded linear operators on a complex Hilbert space ${\mathscr H}$. In this paper, we present some norm inequalities for sums of operators which are a generalization of some recent…
By the help of power series f we can naturally construct another power series that has as coefficients the absolute values of the coefficients of f. Utilising these functions we prove some inequalities for the spectral radius of the bounded…
We obtain upper bounds for the numerical radius of a product of Hilbert space operators which improve on the existing upper bounds. We generalize the numerical radius inequalities of $n\times n$ operator matrices by using non-negative…
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…
New upper and lower bounds for the numerical radii of Hilbert space operators are given. Among our results, we prove that if $A\in \mathcal{B} \left( \mathcal{H}\right) $ is a hyponormal operator, then for all non-negative non-decreasing…
It is shown that the numerical range of a linear operator operator in a Hilbert space is a (complete) $(1{+}\sqrt2)$-spectral set. The proof relies, among other things, in the behavior of the Cauchy transform of the conjugates of…
Let ($\mathcal{H}, \langle . , .\rangle )$ be a complex Hilbert space and $A$ be a positive bounded linear operator on it. Let $w_A(T)$ be the $A$-numerical radius and $\|T\|_A$ be the $A$-operator seminorm of an operator $T$ acting on the…