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The Bloch Space on the Unit Ball of a Hilbert Space: Maximality and Multipliers
Acta Mathematica Scientia ( IF 1.2 ) Pub Date : 2021-04-19 , DOI: 10.1007/s10473-021-0316-9 Pablo Galindo , Mikael Lindström
中文翻译:
希尔伯特空间单位球上的布洛赫空间:极大值和乘数
更新日期:2021-04-19
Acta Mathematica Scientia ( IF 1.2 ) Pub Date : 2021-04-19 , DOI: 10.1007/s10473-021-0316-9 Pablo Galindo , Mikael Lindström
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.
中文翻译:
希尔伯特空间单位球上的布洛赫空间:极大值和乘数
我们证明,与有限维情况一样,希尔伯特空间的单位球上的Bloch函数空间在非常温和的条件下包含自同构不变的任何解析函数半Banach空间。表征了此类Bloch空间的乘法器,并描述了其某些光谱特性。