Isometric composition operators on weighted Dirichlet space
نویسندگان
چکیده
منابع مشابه
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,...
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In this paper, we characterise the analytic functions φ mapping the open unit disk ∆ into itself whose induced composition operator Cφ : f 7→ f ◦ φ is an isometry on the Bloch space. We show that such functions are either rotations of the identity function or have a factorisation φ = gB where g is a non-vanishing analytic function from ∆ into the closure of ∆, and B is an infinite Blaschke prod...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 2016
ISSN: 0011-4642,1572-9141
DOI: 10.1007/s10587-016-0235-4