Multi-valued weighted composition operators on Fock space

Normal and isometric weighted composition operators on the Fock space

We obtain new and simple characterizations for the boundedness and compactness of weighted composition operators on the Fock space over C. We also describe all weighted composition operators that are normal or isometric.

Fredholm Weighted Composition Operators on Dirichlet Space

Let H be a Hilbert space of analytic functions on the unit disk D. For an analytic function ψ on D, we can define the multiplication operator Mψ : f → ψf, f ∈ H. For an analytic selfmapping φ of D, the composition operator Cφ defined on H as Cφf f ◦ φ, f ∈ H. These operators are two classes of important operators in the study of operator theory in function spaces 1–3 . Furthermore, for ψ and φ,...

On reducibility of weighted composition operators

In this paper, we study two types of the reducing subspaces for the weighted composition operator $W: frightarrow ucdot fcirc varphi$ on $L^2(Sigma)$. A necessary and sufficient condition is given for $W$ to possess the reducing subspaces of the form $L^2(Sigma_B)$ where $Bin Sigma_{sigma(u)}$. Moreover, we pose some necessary and some sufficient conditions under which the subspaces of the form...

A Note on Weighted Composition Operators on L^p-Spaces

Weighted Composition Operators on Weighted Spaces of Vector-valued Analytic Functions

Let V be an arbitrary system of weights on an open connected subset G of CN (N ≥ 1) and let B (E) be the Banach algebra of all bounded linear operators on a Banach space E. Let HVb (G, E) and HV0 (G, E) be the weighted locally convex spaces of vector-valued analytic functions. In this paper, we characterize self-analytic mappings φ : G → G and operator-valued analytic mappings Ψ : G → B (E) whi...