Reflexive representability and stable metrics
Abstract
It is well-known that a topological group can be represented as a group of isometries of a reflexive Banach space if and only if its topology is induced by weakly almost periodic functions (see \cite{Shtern:CompactSemitopologicalSemigroups}, \cite{Megrelishvili:OperatorTopologies} and \cite{Megrelishvili:TopologicalTransformations}). We show that for a metrisable group this is equivalent to the property that its metric is uniformly equivalent to a stable metric in the sense of Krivine and Maurey (see \cite{Krivine-Maurey:EspacesDeBanachStables}). This result is used to give a partial negative answer to a problem of Megrelishvili.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2009
- DOI:
- 10.48550/arXiv.0901.1003
- arXiv:
- arXiv:0901.1003
- Bibcode:
- 2009arXiv0901.1003B
- Keywords:
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- Mathematics - Logic;
- 43A60;
- 22A10;
- 46B20
- E-Print:
- doi:10.1007/s00209-009-0612-x