Related papers: Numerical radius inequalities concerning with alge…
In this article, we proved upper bounds for numerical radius of bounded linear operator and product of operators which generalize and improve existing inequalities. We also obtain a numerical radius inequality of invertible operator using…
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…
We obtain new lower and upper bounds for the numerical radius of a bounded linear operator $A$ on a complex Hilbert space, which refine the existing ones. In particular, if $w(A)$ and $\|A\|$ denote the numerical radius and operator norm of…
In this article, we present new inequalities for the numerical radius of the sum of two Hilbert space operators. These new inequalities will enable us to obtain many generalizations and refinements of some well known inequalities, including…
In this work, an improvement of H\"{o}lder-McCarty inequality is established. Based on that, several refinements of the generalized mixed Schwarz inequality are obtained. Consequently, some new numerical radius inequalities are proved. New…
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…
This paper establishes several new inequalities for the $A$-norm and $A$-numerical radius of operator sums in semi-Hilbertian spaces, significantly advancing the existing theory. We present two fundamental refinements of the generalized…
The main goal of this paper is to present new bounds for certain inner products in Hilbert spaces, with applications to the numerical radius and the operator norm. The obtained results significantly improve earlier results in 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…
Several upper and lower bounds for the numerical radius of $2 \times 2$ operator matrices are developed which refine and generalize the earlier related bounds. In particular, we show that if $B,C$ are bounded linear operators on a complex…
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…
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 $A$ be a bounded linear operator defined on a complex Hilbert space and let $|A|=(A^*A)^{1/2}$ be the positive square root of $A$. Among other refinements of the well known numerical radius inequality $w^2(A)\leq \frac12 \|A^*A+AA^*\|$,…
This study utilizes Orlicz functions to provide refined lower and upper bounds on the q-numerical radius of an operator acting on a Hilbert space. Additionally, the concept of q-sectorial matrices is introduced and further bounds for the…
Let $\mathbb{B}(\mathcal{H})$ be the algebra of all bounded linear operators on a Hilbert space $\mathcal{H}$ and let $N(\cdot)$ be a norm on $\mathbb{B}(\mathcal{H})$. For every $0\leq \nu \leq 1$, we introduce the $w_{_{(N,\nu)}}(A)$ as…
Let $T$ be a bounded linear operator on a complex Hilbert space $\mathscr{H}.$ We obtain various lower and upper bounds for the numerical radius of $T$ by developing the Euclidean operator radius bounds of a pair of operators, which are…
In this study, the classical results on the joint numerical radius for $n$-tuples of Hilbert space operators are extended to the setting of the joint $(f,\delta)$-numerical radius. New and diverse contributions to this area are provided,…
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 $ \mathbb{B}(\mathscr{H})$ represent the $C^*$-algebra, which consists of all bounded linear operators on $\mathscr{H},$ and let $N ( .) $ be a norm on $ \mathbb{B}(\mathscr{H})$. We define a norm $w_{(N,e)} (. , . )$ on $…
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…