On topological groups with an approximate fixed point property

Cleon S. Barroso; Brice R. Mbombo; Vladimir G. Pestov

On topological groups with an approximate fixed point property

Group Theory 2021-02-18 v3

Authors: Cleon S. Barroso , Brice R. Mbombo , Vladimir G. Pestov

Abstract

A topological group $G$ has the Approximate Fixed Point (AFP) property on a bounded convex subset $C$ of a locally convex space if every continuous affine action of $G$ on $C$ admits a net $(x_i)$ , $x_i\in C$ , such that $x_{i}-gx_{i}\longrightarrow 0$ for all $g\in G$ . We study the relationship of this property with amenability.

Keywords

amenable groups topological groups affine algebraic geometry

Cite

@article{arxiv.1410.8370,
  title  = {On topological groups with an approximate fixed point property},
  author = {Cleon S. Barroso and Brice R. Mbombo and Vladimir G. Pestov},
  journal= {arXiv preprint arXiv:1410.8370},
  year   = {2021}
}

Comments

16 pages, latex 2e, the final submission to Anais da Academia Brasileira de Ci\^encias with referee's remarks taken into account

On topological groups with an approximate fixed point property

Abstract

Keywords

Cite

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