Open Access
April 2017 Composition operators on the Bloch space of the unit ball of a Hilbert space
Oscar Blasco, Pablo Galindo, Mikael Lindström, Alejandro Miralles
Banach J. Math. Anal. 11(2): 311-334 (April 2017). DOI: 10.1215/17358787-0000005X

Abstract

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.

Citation

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Oscar Blasco. Pablo Galindo. Mikael Lindström. Alejandro Miralles. "Composition operators on the Bloch space of the unit ball of a Hilbert space." Banach J. Math. Anal. 11 (2) 311 - 334, April 2017. https://doi.org/10.1215/17358787-0000005X

Information

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

zbMATH: 1361.32024
MathSciNet: MR3603343
Digital Object Identifier: 10.1215/17358787-0000005X

Subjects:
Primary: 30D45
Secondary: 46E50 , 46G20

Keywords: Bloch function in the ball , Composition operator , infinite-dimensional holomorphy

Rights: Copyright © 2017 Tusi Mathematical Research Group

Vol.11 • No. 2 • April 2017
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