Related papers: On numerical diameters and linear maps
We introduce a new norm on the space of bounded linear operators on a complex Hilbert space, which generalizes the numerical radius norm, the usual operator norm and the modified Davis-Wielandt radius. We study basic properties of this…
We completely characterize the Crawford number attainment set and the numerical radius attainment set of a bounded linear operator on a Hilbert space. We study the intersection properties of the corresponding attainment sets of numerical…
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.
This paper introduces and investigates the concept of the $q$-numerical range for tuples of bounded linear operators in Hilbert spaces. We establish various inequalities concerning the $q$-numerical radius associated with these operator…
We establish new integral inequalities for the numerical radius and the operator norm of bounded linear operators on Hilbert spaces. Our results refine classical triangle-type and operator matrix inequalities by incorporating convex…
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…
The diamond and completely bounded norms for linear maps play an increasingly important role in quantum information science, providing fundamental stabilized distance measures for differences of quantum operations. Based on the theory of…
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.…
We refine a recent result of Drury concerning the optimal ratio between the norm and numerical radius of a bounded linear operator $T$ with numerical range lying in a sector of a circular disk. In particular, characterization is given to…
Researchers have identified complex matrices $A$ such that a bounded linear operator $B$ acting on a Hilbert space will admit a dilation of the form $A \otimes I$ whenever the numerical range inclusion relation $W(B) \subseteq W(A)$ holds.…
We study the typical behavior of bounded linear operators on infinite dimensional complex separable Hilbert spaces in the norm, strong-star, strong, weak polynomial and weak topologies. In particular, we investigate typical spectral…
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…
Let $f$ be a symmetric norm on ${\mathbb R}^n$ and let ${\mathcal B}({\mathcal H})$ be the set of all bounded linear operators on a Hilbert space ${\mathcal H}$ of dimension at least $n$. Define a norm on ${\mathcal B}({\mathcal H})$ by…
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…
Motivated by the recent developments of pseudo-Hermitian quantum mechanics, we analyze the structure generated by unbounded metric operators in a Hilbert space. To that effect, we consider the notions of similarity and quasi-similarity…
We obtain a complete characterization of the norm attainment set of a bounded linear functional on a normed space, in terms of a semi-inner-product defined on the space. Motivated by this result, we further apply the concept of…
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…
We give an expression for a generalized numerical radius of Hilbert space operators and then apply it to obtain upper and lower bounds for the generalized numerical radius. We also establish some generalized numerical radius inequalities…
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…
In this paper, we introduce a new semi-norm of operators on a semi-Hilbertian space, which generalizes the A-numerical radius and A-operator semi-norm. We study the basic properties of this semi-norm, including upper and lower bounds for…