Banach Journal of Mathematical Analysis

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

Oscar Blasco, Pablo Galindo, Mikael Lindström, and Alejandro Miralles

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Every analytic self-map of the unit ball of a Hilbert space induces a bounded composition operator on the space of Bloch functions. Necessary and sufficient conditions for compactness of such composition operators are provided, as well as some examples that clarify the connections among such conditions.

Article information

Banach J. Math. Anal., Volume 11, Number 2 (2017), 311-334.

Received: 14 March 2016
Accepted: 30 May 2016
First available in Project Euclid: 28 January 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 30D45: Bloch functions, normal functions, normal families
Secondary: 46E50: Spaces of differentiable or holomorphic functions on infinite- dimensional spaces [See also 46G20, 46G25, 47H60] 46G20: Infinite-dimensional holomorphy [See also 32-XX, 46E50, 46T25, 58B12, 58C10]

composition operator Bloch function in the ball infinite-dimensional holomorphy


Blasco, Oscar; Galindo, Pablo; Lindström, Mikael; Miralles, Alejandro. Composition operators on the Bloch space of the unit ball of a Hilbert space. Banach J. Math. Anal. 11 (2017), no. 2, 311--334. doi:10.1215/17358787-0000005X.

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