منابع مشابه
Isometric weighted composition operators
A composition operator is an operator on a space of functions defined on the same set. Its action is by composition to the right with a fixed selfmap of that set. A composition operator followed by a multiplication operator is called a weighted composition operator. In this paper, we study when weighted composition operators on the Hilbert Hardy space of the open unit disc are isometric. We fin...
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Let φ be a holomorphic self-map of a bounded homogeneous domain D in C. In this work, we show that the composition operator Cφ : f 7→ f ◦ φ is bounded on the Bloch space B of the domain and provide estimates on its operator norm. We also give a sufficient condition for φ to induce an isometry on B. This condition allows us to construct non-trivial examples of isometric composition operators in ...
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We consider a generalization of isometric Hilbert space operators to the multivariable setting. We study some of the basic properties of these tuples of commuting operators and we explore several examples. In particular, we show that the d-shift, which is important in the dilation theory of d-contractions (or row contractions), is a d-isometry. As an application of our techniques we prove a the...
متن کاملNormal 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.
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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: Operators and Matrices
سال: 2017
ISSN: 1846-3886
DOI: 10.7153/oam-11-56