Compact composition operators on the Bloch space
نویسندگان
چکیده
منابع مشابه
Compact Composition Operators on Bmoa and the Bloch Space
We give a new and simple compactness criterion for composition operators Cφ on BMOA and the Bloch space in terms of the norms of φ in the respective spaces.
متن کاملCompact Composition Operators on Bloch Type Spaces
In this paper we characterize continuity and compactness of composition operators Cφ mapping the α-Bloch space into the μ-Bloch space, where μ is a weight defined on the unit disk D, in term of certain expression that involve the n-power of the symbol φ.
متن کاملCompact Differences of Composition Operators from Bloch Space to Bounded Holomorphic Function Space in the Polydisc
Abstract. Let φ and ψ be holomorphic self-maps of the unit polydisc U in the n-dimensional complex space, and denote by Cφ and Cψ the induced composition operators. This paper gives some simple estimates of the essential norm for the difference of composition operators Cφ − Cψ from Bloch space to bounded holomorphic function space in the unit polydisc. Moreover the compactness of the difference...
متن کاملCharacterisation of the Isometric Composition Operators on the Bloch Space
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...
متن کاملCompact Composition Operators between Bloch Type Spaces in the Polydisk
and Applied Analysis 3 The following lemma is the crucial criterion for the compactness of Cφ, whose proof is an easy modification of the proof of Proposition 3.11 in 1 . Lemma 2.4. Assume that φ is a holomorphic self-map of D. Then Cφ : Bp → Bq is compact if and only if Cφ is bounded and for any bounded sequence {fm}m∈N in Bp which converges to zero uniformly on compact subsets of D, we have ∥...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1995
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-1995-1273508-x