Weighted composition operators on the Dirichlet space: boundedness and spectral properties
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 investigate composition operators induced on the Dirichlet space by linear fractional maps. We characterize the essential normality in this setting, obtain conditions for the linear fractional symbols φ and ψ of the unit disc for which CφC∗ ψ or C ∗ ψCφ is compact, and investigate the shape of the numerical range for linear fractional composition operators induced on the Dirich...
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In this paper, we obtain a sucient condition for boundedness of composition operators betweenweighted spaces of holomorphic functions on the upper half-plane whenever our weights are standardanalytic weights, but they don't necessarily satisfy any growth condition.
متن کاملEssential norms of weighted composition operators on the space H∞ of Dirichlet series
We estimate the essential norm of a weighted composition operator relatively to the class of Dunford-Pettis operators or the class of weakly compact operators, on the space H∞ of Dirichlet series. As particular cases, we obtain the precise value of the generalized essential norm of a composition operator and of a multiplication operator.
متن کاملBoundedness, Compactness and Schatten-class Membership of Weighted Composition Operators
The boundedness and compactness of weighted composition operators on the Hardy space H of the unit disc is analysed. Particular reference is made to the case when the self-map of the disc is an inner function. Schattenclass membership is also considered; as a result, stronger forms of the two main results of a recent paper of Gunatillake are derived. Finally, weighted composition operators on w...
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2015
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-015-1195-y