Related papers: Topological structures of generalized Volterra-typ…
We study the topology of X given that Cp(X) injects into Cp(Y), where Y is compact. We first show that if Cp over a GO-space (="subspace of a lineraly ordered space") injects into Cp over a compactum, then the Dedekind remainder of the…
The Korenblum space, often referred to as a growth space, is a special type of analytic function space. This paper investigates the properties of the difference of composition operators on the Korenblum space over the product of upper half…
We give a few observations on different types of bounded operators on a topological vector space X and their relations with compact operators on X. In particular, we investigate when these bounded operators coincide with compact operators.…
Conditions for linear integral operators on $L_p$ over measure spaces to satisfy the polynomial covariance type commutation relations are described in terms of defining kernels of the corresponding integral operators. Representation by…
We give a geometric characterization of the elements of a TRO that can be represented as compact operators by a faithful representation of the TRO.
In this paper, we study operator-theoretic properties (boundedness and compactness) of Hankel operators on the Fock-sobolev spaces $ \mathscr{F}^{p,m} $ in terms of $ \mathcal{BMO}_r^p $ and $ \mathcal{VMO}_r^p $ spaces, respectively, for a…
In this work we establish sharp kernel conditions ensuring that the corresponding integral operators belong to Schatten-von Neumann classes. The conditions are given in terms of the spectral properties of operators acting on the kernel. As…
The boundedness and compactness of weighted composition operators on the Hardy space ${\mathcal H}^2$ of the unit disc is analysed. Particular reference is made to the case when the self-map of the disc is an inner function. Schatten-class…
We study the spectrum of the Volterra composition operator in the space $L_2[0,1]$
Let $n\ge 1$ and $\varphi: \mathbb{D}^n\to\mathbb{D}$ be a holomorphic function, where $\mathbb{D}$ denotes the open unit disk of $\mathbb{C}$. Let $\Theta: \mathbb{D} \to \mathbb{D}$ be an inner function and $K^p_\Theta$, $p>0$, denote the…
We obtain a complete characterization of the bounded Hausdorff operators acting on a Fock space $F^p_\alpha$ and taking its values into a larger one $F^q_\alpha,\ 0 < p \leq q \leq \infty,$ as well as some necessary or sufficient conditions…
Let E be a locally solid vector lattice. In this paper, we consider two particular vector subspaces of the space of all order bounded operators on E. With the aid of two appropriate topologies, we show that under some conditions, they…
The Carleson measures for weighted Dirichlet spaces had been characterized by Girela and Pel\'{a}ez, who also characterized the boundedness of Volterra type operators between weighted Dirichlet spaces. However, their characterizations for…
In this paper, we study the weighted composition operator on the Fock space $\mf$ of slice regular functions. First, we characterize the boundedness and compactness of the weighted composition operator. Subsequently, we describe all the…
We give a simplified proof of the Berger-Coburn theorem on the boundedness of Toeplitz operators and extend this theorem to the setting of $p$-Fock spaces $(1\leq p \leq \infty)$. We present an overview of recent results by various authors…
Using tools from quantum harmonic analysis, we show that the domain of the Laplacian of an operator is dense in the Toeplitz algebra over the Fock space $\mathcal{F}^2(\mathbb{C}^n)$. As an application, we provide a simplified treatment of…
We generalize, on one hand, some results known for composition operators on Hardy spaces to the case of Hardy-Orlicz spaces $H^\Psi$: construction of a "slow" Blaschke product giving a non-compact composition operator on $H^\Psi$;…
An operator $T$ from vector lattice $E$ into vector topology $(F,\tau)$ is said to be order-to-topology continuous whenever $x_\alpha\xrightarrow{o}0$ implies $Tx_\alpha\xrightarrow{\tau}0$ for each $(x_\alpha)_\alpha\subset E$. The…
In this note, we consider a class of composition operators on Lebesgue spaces with variable exponents over metric measure spaces. Taking advantage of the compatibility between the metric-measurable structure and the regularity properties of…
We prove variants of Wiener's Tauberian theorem in the framework of quantum harmonic analysis, i.e. for convolutions between an absolutely integrable function and a trace class operator, or of two trace class operators. Our results include…