Related papers: More on $\omega$-orthogonality and $\omega$-parall…
In this work, the mixed Schwarz inequality for semi-Hilbertian space operators is proved. Namely, for every positive Hilbert space operator $A$. If $f$ and $g$ are nonnegative continuous functions on $\left[0,\infty\right)$ satisfying…
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.
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…
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…
In this paper, more inequalities between the operator norm and its numerical radius, for the class of normal operators, are established. Some of the obtained results are based on recent reverse results for the Schwarz inequality in Hilbert…
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…
The purpose of the article is to generalize the concept of approximate Birkhoff-James orthogonality, in the semi-Hilbertian structure. Given a positive operator $ A $ on a Hilbert space $ \mathbb{H}, $ we define $ (\epsilon,A)- $approximate…
In this paper we characterize Birkhoff-James orthogonality of linear operators defined on a finite dimensional real Banach space $ \mathbb{X}. $ We also explore the symmetry of Birkhoff-James orthogonality of linear operators defined on $…
The two well-known numerical radius inequalities for the tensor product $A \otimes B$ acting on $\mathbb{H} \otimes \mathbb{K}$, where $A$ and $B$ are bounded linear operators defined on complex Hilbert spaces $\mathbb{H} $ and $…
Several unitarily invariant norm inequalities and numerical radius inequalities for Hilbert space operators are studied. We investigate some necessary and sufficient conditions for the parallelism of two bounded operators. For a finite rank…
Given a Hilbert module $H$ over a $C^*$-algebra, let $\mathcal{L}(H)$ be the set of all adjointable operators on $H$. For each $T\in\mathcal{L}(H)$, its numerical radius is defined by $w(T)=\sup\big\{\|\langle Tx, x \rangle\|: x\in H,…
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…
There are two notions of approximate Birkhoff-James orthogonality in a normed space. We characterize both the notions of approximate Birkhoff-James orthogonality in the space of bounded linear operators defined on a normed space. A complete…
If $A,B$ are bounded linear operators on a complex Hilbert space, then % $w(A) \leq \frac{1}{2}\left( \|A\|+\sqrt{r\left(|A||A^*|\right)}\right)$ and $w(AB \pm BA)\leq 2\sqrt{2}\|B\|\sqrt{ w^2(A)-\frac{c^2(\Re (A))+c^2(\Im (A))}{2} },$…
Let $(\mathcal{H}, [\cdot, \cdot ])$ be a Hilbert space and $K(\mathcal{H})$ be the $C^*$-algebra of compact operators on $\mathcal{H}$. In this paper, we present some characterizations of the norm-parallelism for elements of a Hilbert…
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 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 present some new upper and lower bounds for the numerical radius of bounded linear operators on a complex Hilbert space and show that these are stronger than the existing ones. In particular, we prove that if $A$ is a bounded linear…
This article is devoted to studying some new numerical radius inequalities for Hilbert space operators. Our analysis enables us to improve an earlier bound of numerical radius due to Kittaneh.
We present some properties of orthogonality and relate them with support disjoint and norm inequalities in p Schatten ideals. In addition, we investigate the problem of characterization of norm parallelism for bounded linear operators. We…