Related papers: Composition operators between two different bilate…
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…
This paper explores a version of the classical Ces`aro integral operator for the Lebesgue space L2(0, 1) where we discuss its norm, adjoint, spectral properties, and invariant subspaces. An important tool will be semigroups of weighted…
We provide complete characterisations of nuclear weighted composition operators between two distinct $L^p(\mu)$-spaces, where $1\leq p<\infty$. As a consequence, when the underlying measure space is non-atomic, the only nuclear weighted…
We investigate composition-differentiation operators acting on the space $S^2$, the space of analytic functions on the open unit disk whose first derivative is in $H^2$. Specifically, we determine characterizations for bounded and compact…
We give in this short paper the exact value for norms of two operators of Hardy-Sobolev type acting between two weight Grand Lebesgue Space (GLS) based on the whole multidimensional Euclidean space.
We obtain necessary and sufficient conditions for the composition and weighted composition operator and product of composition operators to be isometry and unitary on $H_{E}(\xi).$ With the help of counter example we also prove that the…
In this paper we study connections between composition operators on Sobolev spaces and mappings defined by $p$-moduli inequalities ($p$-capacity inequalities). We prove that weighted moduli inequalities lead to composition operators on…
Some new inequalities for the norm and the numerical radius of composite operators generated by a pair of operators are given.
In this paper we give connections between mappings which generate bounded composition operators on Sobolev spaces and $Q$-mappings. On this base we obtain measure distortion properties $Q$-homeomorphisms. Using the composition operators on…
We study weighted composition operators on Hilbert spaces of analytic functions on the unit ball with kernels of the form $(1-<z,w>)^{-\gamma}$ for $\gamma>0$. We find necessary and sufficient conditions for the adjoint of a weighted…
We study composition operators on the Hardy space $\mathcal{H}^2$ of Dirichlet series with square summable coefficients. Our main result is a necessary condition, in terms of a Nevanlinna-type counting function, for a certain class of…
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…
We give examples of results on composition operators connected with lens maps. The first two concern the approximation numbers of those operators acting on the usual Hardy space $H^2$. The last ones are connected with Hardy-Orlicz and…
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…
A linear relation, i.e., a multivalued operator $T$ from a Hilbert space ${\mathfrak H}$ to a Hilbert space ${\mathfrak K}$ has Lebesgue type decompositions $T=T_{1}+T_{2}$, where $T_{1}$ is a closable operator and $T_{2}$ is an operator or…
Continuing the study initiated in our earlier article [7], this paper aims to characterize various continuity properties of nonlinear composition operators acting on some sequence spaces, giving special attention to the space of sequences…
We consider the composition of operators with non-closed range in Hilbert spaces and how the nature of ill-posedness is affected by their composition. Specifically, we study the \mbox{Hausdorff-,} Ces\`{a}ro-, integration operator, and…
We study the existence of the product of two weighted modulation spaces. For this purpose we discuss two different strategies. The more simple one allows transparent proofs in various situations. However, our second method allows a closer…
In this paper, first we characterize closedness of range of the finite sum of weighted composition operators between different Lp-spaces. Then we discuss polar decomposition and invertibility of these operators.
In this note unbounded hyperexpansive weighted composition operators are investigated. AS a consequence unbounded hyperexpansive multiplication and composition operators are characterized.