Related papers: Exact essential norm of generalized Hilbert matrix…

The main aim of this article is to establish several $p$-numerical radius inequalities via the $(f,g)$-Aluthge transform of Hilbert space operators and operator matrices. Furthermore, various classical numerical radius and norm inequalities…

By H\"ormander's $L^2$-method, we study the operator $\alpha \partial^k \bar{\partial}^{k} + \beta \bar{\partial}^k +\gamma \partial^k + c$ for any order $k$ with $\alpha, \beta, \gamma \in \mathbb{R}$ such that $(\alpha, \beta, \gamma)…

In this paper we will show how the boundedness condition for the weighted composition operators on a class of spaces of analytic functions on the open right complex half-plane called Zen spaces (which include the Hardy spaces and weighted…

After a review of the reproducing kernel Banach space framework and semi-inner products, we apply the techniques to the setting of Hardy spaces $H^p$ and Bergman spaces $A^p$, $1<p<\infty$, on the unit ball in $\mathbb{C}^n$, as well as the…

We prove several numerical radius inequalities for linear operators in Hilbert spaces. It is shown, among other inequalities, that if $A$ is a bounded linear operator on a complex Hilbert space, then \[\omega \left( A \right)\le…

We consider Volterra-type integration operators $T_g$ between Bergman spaces induced by weights $\omega$ satisfying a doubling property. We derive estimates for the operator norms, essential and weak essential norms of $T_g: A_\omega^p \to…

Let $\mathcal{B}(\mathcal{H})$ denote the Banach algebra of all bounded linear operators acting on complex Hilbert spaces $\mathcal{H}$. In this paper, we first establish several sharply refined versions of Bohr's inequality analogues with…

In this paper we initiate the study of absolute summability for big and little Hankel operators $ H_f^\beta,h_f^\beta:A_\alpha^p(\mathbb{B}_n)\to L^q(\mathbb{B}_n,dv_\beta), $ acting between weighted Bergman and weighted Lebesgue spaces on…

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 $…

We compare the rate of decay of singular numbers of a given composition operator acting on various Hilbert spaces of analytic functions on the unit disk $\D$. We show that for the Hardy and Bergman spaces, our results are sharp. We also…

We present several operator and norm inequalities for Hilbert space operators. In particular, we prove that if $A_{1},A_{2},...,A_{n}\in {\mathbb B}({\mathscr H})$, then…

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…

In this article, we present some new inequalities for numerical radius of Hilbert space operators via convex functions. Our results generalize and improve earlier results by El-Haddad and Kittaneh. Among several results, we show that if…

There has been a great deal of work done in recent years on weighted Bergman spaces $\apa$ on the unit ball $\bn$ of $\cn$, where $0<p<\infty$ and $\alpha>-1$. We extend this study in a very natural way to the case where $\alpha$ is {\em…

We study integral operators on the space of square-integrable functions from a compact set, $X$, to a separable Hilbert space, $H$. The kernel of such an operator takes values in the ideal of Hilbert-Schmidt operators on $H$. We establish…

In this research article the necessary and sufficient conditions for the norm of composition operator $C_{\Phi}$ on $\mathcal{A}_{\alpha}^2(H)$ to be one are obtained. Moreover, $C_{\Phi}$ is unitary on $\mathcal{A}_{\alpha}^2(H)$ if and…

We get the sharp bound for weak type $(1,1)$ inequality for $n$-dimensional Hardy operator. Moreover, the precise norms of generalized Hardy operators on the type of Campanato spaces are obtained. As applications, the corresponding norms of…

In this paper we study mapping properties of Toeplitz-like operators on weighted Bergman spaces of bounded strongly pseudconvex domains in $\mathbb{C}^n$. In particular we prove that a Toeplitz operator built using as kernel a weighted…

For a real number $\alpha$ the Hilbert spaces $\mathscr{D}_\alpha$ consists of those Dirichlet series $\sum_{n=1}^\infty a_n/n^s$ for which $\sum_{n=1}^\infty |a_n|^2/[d(n)]^\alpha < \infty$, where $d(n)$ denotes the number of divisors of…

We introduce the notions of L(H)-valued norms and Banach spaces with respect to L(H)-valued norms. In particular, we introduce Hilbert spaces with respect to L(H)-valued inner products. In addition, we provide several fundamental examples…