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The Bloch Space on the Unit Ball of a Hilbert Space: Maximality and Multipliers

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Abstract

We prove that, as in the finite dimensional case, the space of Bloch functions on the unit ball of a Hilbert space contains, under very mild conditions, any semi-Banach space of analytic functions invariant under automorphisms. The multipliers for such Bloch space are characterized and some of their spectral properties are described.

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Authors and Affiliations

  1. Departamento de Análisis Matemático, Universidad de Valencia, C/Dr. Moliner 50, 46.100, Burjasot, Valencia, Spain

    Pablo Galindo

  2. Department of Mathematics, Abo Akademi University, FI-20500, Åbo, Finland

    Mikael Lindström

Authors
  1. Pablo Galindo
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  2. Mikael Lindström
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Corresponding authors

Correspondence to Pablo Galindo or Mikael Lindström.

Additional information

The first author is partially supported by Spanish MINECO/FEDER PGC2018-094431-B-I00. The second author is partially supported by the Academy of Finland Project 296718.

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Galindo, P., Lindström, M. The Bloch Space on the Unit Ball of a Hilbert Space: Maximality and Multipliers. Acta Math Sci 41, 899–906 (2021). https://doi.org/10.1007/s10473-021-0316-9

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  • DOI: https://doi.org/10.1007/s10473-021-0316-9

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