Proper metrics on locally compact groups, and proper affine isometric actions on Banach spaces

Details Proper metrics on locally compact groups, and proper affine isometric actions on Banach spaces Proper metrics on locally compact groups, and proper affine isometric actions on Banach spaces

Publishing date

2006-06-30

URL

arxiv.org/abs/math/0606794v1

Science

Mathematics

Field

Operator Algebras

Type

Scientific paper

Abstract

In this article it is proved, that every locally compact second countable group has a left invariant metric d, which generates the topology on G, and which is proper, ie. every closed d-bounded set in G is compact. Moreover, we obtain the following extension of a result due to N. Brown and E. Guentner: Every locally compact second countable $G$ admits a proper affine action on the reflexive and strictly convex Banach space $\bigoplus^{\infty}_{n=1} L^{2n}(G, d\mu),$ where the direct sum is taken in the $l^2$-sense.

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