Embedding a topological group into its WAP-compactification
Volume 193 / 2009
Studia Mathematica 193 (2009), 99-108
MSC: 43A60, 22A10, 46B20.
DOI: 10.4064/sm193-2-1
Abstract
We prove that the topology of the additive group of the Banach space $c_0$ is not induced by weakly almost periodic functions or, what is the same, that this group cannot be represented as a group of isometries of a reflexive Banach space. We show, in contrast, that additive groups of Schwartz locally convex spaces are always representable as groups of isometries on some reflexive Banach space.
