Related papers: Further results on $\mathbb{A}$-numerical radius i…

The concepts of weighted numerical radius has been defined in recent times. In this article, we obtain several upper bound for weighted numerical radius of operators and $2 \times 2$ operator matrices which generalize and improves some well…

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…

In this paper we derive necessary and sufficient conditions for the nonnegativity of Moore-Penrose inverses of unbounded Gram operators between real Hilbert spaces. These conditions include statements on acuteness of certain closed convex…

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…

In this paper we study some geometric properties like parallelism, orthogonality and semi-rotundity in the space of bounded linear operators. We completely characterize parallelism of two compact linear operators between normed linear…

We prove that for a right linear bounded normal operator on a quaternionic Hilbert space (quaternionic bounded normal operator) the norm and the numerical radius are equal. As a consequence of this result we give a new proof of the known…

Let $A$ be a positive (semidefinite) operator on a complex Hilbert space $\mathcal{H}$ and let $\mathbb{A}=\left(\begin{array}{cc} A & O O & A \end{array}\right).$ We obtain upper and lower bounds for the $A$-Davis-Wielandt radius of…

Some new inequalities for the norm and the numerical radius of composite operators generated by a pair of operators are given.

Let $A_{i}\ (i=1, 2, ..., k)$ be bounded linear operators on a Hilbert space. This paper aims to show characterizations of operator order $A_{k}\geq A_{k-1}\geq...\geq A_{2}\geq A_{1}>0$ in terms of operator inequalities. Afterwards, an…

Let $K,\,H$ be Hilbert spaces and let $L(K,H)$ denote the set of all bounded linear operators from $K$ to $H$. Let $A \in L(H)\triangleq L(H,H)$ with $R(A)$ closed and $X,Y \in L(K,H)$ with $R(X)\subseteq R(A),R(Y)\subseteq R(A^*)$. In this…

We describe continuity properties of the multivalued inverse of the numerical range map $f_A:x \mapsto \left\langle Ax, x \right\rangle$ associated with a linear operator $A$ defined on a complex Hilbert space $\mathcal{H}$. We prove in…

We develop several upper and lower bounds for the $A$-Euclidean operator radius of $2$-tuple operators admitting $A$-adjoint, and show that they refine the earlier related bounds. As an application of the bounds developed here, we obtain…

Let $\mathcal{H}$ be a complex Hilbert space and let $\big\{A_{n}\big\}_{n\geq 1}$ be a sequence of bounded linear operators on $\mathcal{H}$. Then a bounded operator $B$ on a Hilbert space $\mathcal{K} \supseteq \mathcal{H}$ is said to be…

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…

Let $A$ be a positive operator on a Hilbert space $\mathcal{H}$ with $0<m\leq A\leq M$ and $X$ and $Y$ are two isometries on $\mathcal{H}$ such that $X^{*}Y=0$. For every 2-positive linear map $\Phi$, define…

Let $A$ be a positive definite operator on a Hilbert space $H$, and $|||.|||$ be a unitarily invariant norm on $B(H)$. We show that if $f$ is an operator monotone function on $(0,\infty)$ and $n\in \mathbb{N}$, then $|||D^n…

In this article, we present some new inequalities for the numerical radius of products of Hilbert space operators and the generalized Aluthge transform. In particular, we show some upper bounds for $\omega(ABC+DEF)$ using the celebrated…

We consider the question of, given operators $A$, $Z$ and a sequence of invertible operators $U_n\to Z$, whether the sequence $U_nAU_n^{-1}$ is bounded in norm, as well as generalizations of this where $U_nAU_n^{-1}$ is modified by some…

We obtain bounds for the numerical radius of $2 \times 2$ operator matrices which improve on the existing bounds. We also show that the inequalities obtained here generalize the existing ones. As an application of the results obtained here…

We establish new upper bounds for Berezin number and Berezin norm of operator matrices, which are refinements of the existing bounds. Among other bounds, we prove that if $A=[A_{ij}]$ is an $n\times n$ operator matrix with…