Composition operators on the Bloch space of the unit ball of a Hilbert space

Let ϕ(z) = (ϕ1(z),…,ϕn(z)) be a holomorphic self-map of B and ψ(z) a holomorphic function on B, where B is the unit ball of ℂn. Let 0 < p, s < +∞, -n - 1 < q < +∞, q+s > -1 and α ≥ 0, this paper characterizes boundedness and compactness of weighted composition operator Wψ,ϕ induced by ϕ and ψ between the space F(p, q, s) and α-Bloch space [Formula: see text].

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Essential Norms of Weighted Composition Operators from theα-Bloch Space to a Weighted-Type Space on the Unit Ball

Abstract and Applied Analysis ◽

10.1155/2008/279691 ◽

2008 ◽

Vol 2008 ◽

pp. 1-11 ◽

Cited By ~ 39

Author(s):

Stevo Stević

Keyword(s):

Unit Ball ◽

Composition Operators ◽

Bloch Space ◽

Weighted Composition Operator ◽

Essential Norm ◽

Weighted Composition Operators ◽

Lower And Upper Bounds ◽

Type Space ◽

Weighted Composition ◽

Weighted Type

This paper finds some lower and upper bounds for the essential norm of the weighted composition operator fromα-Bloch spaces to the weighted-type spaceHμ∞on the unit ball for the caseα≥1.

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Volterra composition operators from generalized weighted weighted Bergman spaces toµ-Bloch spaces

Journal of Function Spaces and Applications ◽

10.1155/2009/179381 ◽

2009 ◽

Vol 7 (3) ◽

pp. 225-240 ◽

Cited By ~ 1

Author(s):

Xiangling Zhu

Keyword(s):

Holomorphic Function ◽

Unit Ball ◽

Bergman Space ◽

Composition Operators ◽

Bloch Space ◽

Bergman Spaces ◽

Weighted Bergman Space ◽

Weighted Bergman Spaces ◽

Bloch Spaces

Letφbe a holomorphic self-map andgbe a fixed holomorphic function on the unit ballB. The boundedness and compactness of the operatorTg,φf(z)=∫01f(φ(tz))ℜg(tz)dttfrom the generalized weighted Bergman space into the µ-Bloch space are studied in this paper.

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Spectra of composition operators on algebras of analytic functions on Banach spaces

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210507000819 ◽

2009 ◽

Vol 139 (1) ◽

pp. 107-121 ◽

Cited By ~ 7

Author(s):

P. Galindo ◽

T. W. Gamelin ◽

Mikael Lindström

Keyword(s):

Banach Space ◽

Hilbert Space ◽

Fixed Point ◽

Unit Ball ◽

Banach Spaces ◽

Composition Operator ◽

Composition Operators ◽

Open Unit ◽

Open Unit Ball ◽

Analytic Symbol

Let E be a Banach space, with unit ball BE. We study the spectrum and the essential spectrum of a composition operator on H∞(BE) determined by an analytic symbol with a fixed point in BE. We relate the spectrum of the composition operator to that of the derivative of the symbol at the fixed point. We extend a theorem of Zheng to the context of analytic symbols on the open unit ball of a Hilbert space.

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