Related papers: On Unbounded Composition Operators in $L^2$-Spaces
Unbounded composition operators in $L^2$-space over discrete measure spaces are investigated. Normal, formally normal and quasinormal composition operators acting in $L^2$-spaces of this kind are characterized.
Bounded and unbounded weighted composition operators on $L^2$ spaces over $\sigma$-finite measure spaces are investigated. A variety of questions related to seminormality of such operators are discussed.
A criterion for subnormality of unbounded composition operators in L2-spaces, written in terms of measurable families of probability measures satisfying the so-called consistency condition, is established. It becomes a new characterization…
We prove, by use of inductive techniques, that assorted unbounded composition operators in $L^2$-spaces with matrical symbols are cosubnormal.
In this paper we deal with unbounded composition operators defined in Orlicz spaces. Indeed, we provide some necessary and sufficient condition for densely definedness of composition operators on Orlicz spaces. Also, we will investigate the…
Centered weighted composition operators on $L^2$-spaces are characterized. The characterization is obtained without the assumption that the operator is a product of a multiplication and a composition operator. The concept of spectrally…
We establish necessary and sufficient conditions for boundedness of composition operators on the most general class of Hilbert spaces of entire Dirichlet series with real frequencies. Depending on whether or not the space contains any…
A linear operator $S$ in a complex Hilbert space $\hh$ for which the set $\dzn{S}$ of its $C^\infty$-vectors is dense in $\hh$ and $\{\|S^n f\|^2\}_{n=0}^\infty$ is a Stieltjes moment sequence for every $f \in \dzn{S}$ is said to generate…
This paper investigates composition operators and weighted composition operators on semi-Hilbert spaces induced by positive multiplication operators on \( L^2(\mu) \). Within the framework of \( A \)-adjoint operators, we characterize…
A recent example of a non-hyponormal injective composition operator in an $L^2$-space generating Stieltjes moment sequences, invented by three of the present authors, was built over a non-locally finite directed tree. The main goal of this…
The boundedness (continuity) of composition operators from some function space to another one is significant, though there are few results about this problem. Thus, in this study, we provide necessary and sufficient conditions on the…
The paper deals with unbounded composition operators with infinite matrix symbols acting in $L^2$-spaces with respect to the gaussian measure on $\mathbb{R}^\infty$. We introduce weak cohyponormality classes $\EuScript{S}_{n,r}^*$ of…
We describe the Aluthge transform of an unbounded weighted composition operator acting in an $L^2$-space. We show that its closure is also a weighted composition operator with the same symbol and a modified weight function. We investigate…
In this paper we define $\lambda$-hyponormal operators on an infinite dimensional Hilbert space $\mathcal{H}$ and find a class of $\lambda$-hyponormal operators that can not be hypercyclic. Also, we study closedness of range and…
In this note unbounded hyperexpansive weighted composition operators are investigated. AS a consequence unbounded hyperexpansive multiplication and composition operators are characterized.
In this paper we characterize $m$-isometric and quasi-$m$-isometric weighted composition operators on the Hilbert space $L^2(\mu)$. Also, we find that normal-$m$-isometry and normal quasi-$m$-isometry weighted composition operators have…
In this paper we characterize some basic properties of composition operators on the spaces of harmonic Bloch functions. First we provide some equivalent conditions for boundedness and compactness of composition operators. Then by using…
We study two classes of bounded operators on mixed norm Lebesgue spaces, namely composition operators and product operators. A complete description of bounded composition operators on mixed norm Lebesgue spaces are given. For a certain…
In this paper, we consider composition operators on weighted Hilbert spaces of analytic functions and observe that a formula for the essential norm, give a Hilbert-Schmidt characterization and characterize the membership in Schatten-class…
We study power boundedness and related properties such as mean ergodicity for (weighted) composition operators on function spaces defined by local properties. As a main application of our general approach we characterize when (weighted)…