无不可约Banach表示的阿贝尔拓扑群

V. Pestov
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引用次数: 1

摘要

我们证明了在Banach空间中不允许有非平凡强连续不可约表示的阿贝尔拓扑群。其中包括可分离Hilbert空间上的一些abelian Banach-Lie群和一些幺正群的一元子群。
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Abelian Topological Groups without Irreducible Banach Representations
We exhibit abelian topological groups admitting no nontrivial strongly continuous irreducible representations in Banach spaces. Among them are some abelian Banach-Lie groups and some monothetic subgroups of the unitary group of a separable Hilbert space.
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