Reducing subspaces for a class of multiplication operators on the Dirichlet space
نویسندگان
چکیده
منابع مشابه
Hankel operators and invariant subspaces of the Dirichlet space
The Dirichlet space D is the space of all analytic functions f on the open unit disc D such that f ′ is square integrable with respect to two-dimensional Lebesgue measure. In this paper we prove that the invariant subspaces of the Dirichlet shift are in 1-1 correspondence with the kernels of the Dirichlet-Hankel operators. We then apply this result to obtain information about the invariant subs...
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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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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2009
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-09-09859-1