Related papers: Advanced Refinements of Numerical Radius Inequalit…
We prove several numerical radius inequalities involving positive semidefinite matrices via the Hadamard product and Kwong functions. Among other inequalities, it is shown that if $X$ is an arbitrary $n\times n$ matrix and $A,B$ are…
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…
In this paper, we investigate the spectral radius al- gebras related to the weighted conditional expectation operators on the Hilbert spaces L2(F). We give a large classes of operators on L2(F) that have the same spectral radius algebra. As…
In this paper, we investigate the relation between the Deddens and spectral radius algebras of two bounded linear operators, noting a similarity between them. Additionally, we characterize the Deddens and spectral radius algebras related to…
Let $\mathbf{T}=(T_1,\ldots,T_d)$ be a $d$-tuple of operators on a complex Hilbert space $\mathcal{H}$. The spherical Aluthge transform of $\mathbf{T}$ is the $d$-tuple given by…
We consider the Hilbert-type operator defined by $$ H_{\omega}(f)(z)=\int_0^1 f(t)\left(\frac{1}{z}\int_0^z B^{\omega}_t(u)\,du\right)\,\omega(t)dt,$$ where $\{B^{\omega}_\zeta\}_{\zeta\in\mathbb{D}}$ are the reproducing kernels of the…
This paper explores the concept of approximate Birkhoff-James orthogonality in the context of operators on semi-Hilbert spaces. These spaces are generated by positive semi-definite sesquilinear forms. We delve into the fundamental…
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…
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,…
In this survey, we shall present characterizations of some distinguished classes of Hilbertian bounded linear operators (namely, normal operators, selfadjoint operators, and unitary operators) in terms of operator inequalities related to…
The Menchov-Rademacher inequality is an inequality in harmonic analysis that bounds the $L_2$ norm of a certain maximal operator. It was first established in order to prove almost everywhere convergence of a one-parameter series of…
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.…
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…
We give some new refinements of Heinz inequality and an improvement of the reverse Young's inequality for scalars and we use them to establish new inequalities for operators and the Hilbert-Schmidt norm of matrices. We give a uniformly and…
In this paper, we define a new concept of numerical range $W_{o}(\cdot)$ and prove its basic results. We also define the numerical radius $\omega_{o}(\cdot)$ and prove that $$\omega_{o}(T)\leq||| T|||\leq 2\omega_{o}(T).$$
We present several operator extensions of the Chebyshev inequality for Hilbert space operators. The main version deals with the synchronous Hadamard property for Hilbert space operators. Among other inequalities, it is shown that if…
In this article, we prove several multi-term refinements of Young type inequalities for both real numbers and operators improving several known results. Among other results, we prove \begin{eqnarray*}…
In this article we prove new inequalities for the generalized and the joint spectral radius of bounded sets of positive operators on Banach function and sequence spaces, in particular some inequalities for positive kernel operators that…
We present a necessary and sufficient condition for the norm-parallelism of bounded linear operators on a Hilbert space. We also give a characterization of the Birkhoff--James orthogonality for Hilbert space operators. Moreover, we discuss…
In this paper, we present some upper bounds for unitarily invariant norms inequalities. Among other inequalities, we show some upper bounds for the Hilbert-Schmidt norm. In particular, we prove \begin{align*} \|f(A)Xg(B)\pm…