THE BLOCH SPACE ON THE UNIT BALL OF A HILBERT SPACE: MAXIMALITY AND MULTIPLIERS

doi:10.1007/s10473-021-0316-9

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (3): 899-906.doi: 10.1007/s10473-021-0316-9

THE BLOCH SPACE ON THE UNIT BALL OF A HILBERT SPACE: MAXIMALITY AND MULTIPLIERS

Pablo GALINDO¹, Mikael LINDSTRÖM²

1. Departamento de Análisis Matemático, Universidad de Valencia. C/Dr. Moliner 50. 46. 100, Burjasot, Valencia, Spain;
2. Department of Mathematics, Abo Akademi University. FI-20500 Åbo, Finland

收稿日期:2020-02-20 出版日期:2021-06-25 发布日期:2021-06-07
作者简介:Pablo GALINDO,E-mail:galindo@uv.es;Mikael LINDSTRÖM,E-mail:mikael.lindstrom@abo.fi
基金资助:
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.

THE BLOCH SPACE ON THE UNIT BALL OF A HILBERT SPACE: MAXIMALITY AND MULTIPLIERS

Pablo GALINDO¹, Mikael LINDSTRÖM²

1. Departamento de Análisis Matemático, Universidad de Valencia. C/Dr. Moliner 50. 46. 100, Burjasot, Valencia, Spain;
2. Department of Mathematics, Abo Akademi University. FI-20500 Åbo, Finland

Received:2020-02-20 Online:2021-06-25 Published:2021-06-07
About author:Pablo GALINDO,E-mail:galindo@uv.es;Mikael LINDSTRÖM,E-mail:mikael.lindstrom@abo.fi
Supported by:
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.

摘要/Abstract

摘要： 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.

关键词: Analytic functions on Hilbert space, invariance under automorphisms, multiplier

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.

Key words: Analytic functions on Hilbert space, invariance under automorphisms, multiplier

中图分类号:

30D45

Pablo GALINDO, Mikael LINDSTRÖM. THE BLOCH SPACE ON THE UNIT BALL OF A HILBERT SPACE: MAXIMALITY AND MULTIPLIERS[J]. 数学物理学报(英文版), 2021, 41(3): 899-906.

Pablo GALINDO, Mikael LINDSTRÖM. THE BLOCH SPACE ON THE UNIT BALL OF A HILBERT SPACE: MAXIMALITY AND MULTIPLIERS[J]. Acta mathematica scientia,Series B, 2021, 41(3): 899-906.

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THE BLOCH SPACE ON THE UNIT BALL OF A HILBERT SPACE: MAXIMALITY AND MULTIPLIERS

THE BLOCH SPACE ON THE UNIT BALL OF A HILBERT SPACE: MAXIMALITY AND MULTIPLIERS

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