相关论文: General Numerical Radius for Products of Sectorial…
Let $A$ be a non-zero positive bounded linear operator on a complex Hilbert space $(\mathcal{H},\langle\cdot,\cdot\rangle)$. Let $\omega_A(T)$ denote the $A$-numerical radius of an operator $T$ acting on the semi-Hilbert space…
We obtain several upper and lower bounds for the numerical radius of sectorial matrices. We also develop several numerical radius inequalities of the sum, product and commutator of sectorial matrices. The inequalities obtained here are…
They proved several properties and introduced some inequalities. We continue with the study of this generalized numerical radius and we develop diverse inequalities involving w_N. We also study particular cases with a fixed N(.), for…
It has been shown that if $T$ is a complex matrix, then {\small\begin{align*} \omega(T)&=\frac{1}{n}\sup\left\{|\mathrm{Tr}\ X|;\ X\in W^n(T)\right\}\\ &=\frac{1}{n}\sup\left\{\|X\|_1;\ X\in W^n(T)\right\}\\ &= \sup\left\{ \omega(X);\ X\in…
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 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…
In the present paper, we provide several inequalities for the generalized numerical radius of operator matrices as introduced by A. Abu-omar and F. Kittaneh in [3]. We generalize the convexity and the log-convexity results obtained by M.…
This article focuses on several significant bounds of $q$-numerical radius $w_q(A)$ for sectorial matrix $A$ which refine and generalize previously established bounds. One of the significant bounds we have derived is as follows:…
In this paper, the $q$-numerical radius of operators in semi-Hilbertian spaces is studied. New characterizations are established, and sharp upper and lower bounds for the $q$-numerical radius are derived. Moreover, several inequalities…
The purpose of this note is to present upper bounds estimations for the numerical radius of a products and Hadamard products of special matrices, including sectorial and accretive-dissipative matrices.
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…
We completely characterize Birkhoff-James orthogonality with respect to numerical radius norm in the space of bounded linear operators on a complex Hilbert space. As applications of the results obtained, we estimate lower bounds of…
In this article, firstly, some simple and smoothness properties of the weighted numerical radius and the weighted Crawford number functions are investigated. Then, some generalization formulas for lower and upper bounds of the weighted…
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…
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…
In this paper, we aim to establish a range of numerical radius inequalities. These discoveries will bring us to a recently validated numerical radius inequality and will present numerical radius inequalities that exhibit enhanced precision…
We verify a conjecture on the structure of higher-rank numerical ranges for a wide class of unitary and normal matrices. Using analytic and geometric techniques, we show precisely how the higher-rank numerical ranges for a generic unitary…
In this paper, we begin by showing a new generalization of the celebrated Cauchy-Schwarz inequality for the inner product. Then, this generalization is used to present some bounds for the Euclidean operator radius and the Euclidean operator…
In this paper, we present various inequalities for generalized numerical radius of $2 \times 2$ block matrices for Schatten p-norm. Moreover, we give a refinement of the triangle inequality for the Schatten p-generalized numerical radius.
In this paper we study the joint/generalized spectral radius of a finite set of matrices in terms of its rank-one approximation by singular value decomposition. In the first part of the paper, we show that any finite set of matrices with at…