Abstract
We show that every non-precompact topological group admits a fixed point-free continuous action by affine isometries on a suitable Banach space. Thus, precompact groups are defined by the fixed point property for affine isometric actions on Banach spaces. For separable topological groups, in the above statements it is enough to consider affine actions on one particular Banach space: the unique Banach space envelope
Citation
Lionel Nguyen Van Thé. Vladimir G. Pestov. "Fixed point-free isometric actions of topological groups on Banach spaces." Bull. Belg. Math. Soc. Simon Stevin 17 (1) 29 - 51, February 2010. https://doi.org/10.36045/bbms/1267798497
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