We prove that the topology of the additive group of the Banach space c₀ 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm193-2-1,
author = {Stefano Ferri and Jorge Galindo},
title = {Embedding a topological group into its WAP-compactification},
journal = {Studia Mathematica},
volume = {192},
year = {2009},
pages = {99-108},
zbl = {1179.43003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm193-2-1}
}
Stefano Ferri; Jorge Galindo. Embedding a topological group into its WAP-compactification. Studia Mathematica, Tome 192 (2009) pp. 99-108. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm193-2-1/