Let G be a locally compact group, and consider the weakly almost periodic functionals on M(G), the measure algebra of G, denoted by WAP(M(G)). This is a C*-subalgebra of the commutative C*-algebra M(G)*, and so has character space, say . In this paper, we investigate properties of . We present a short proof that can naturally be turned into a semigroup whose product is separately continuous; at the Banach algebra level, this product is simply the natural one induced by the Arens products. This is in complete agreement with the classical situation when G is discrete. A study of how is related to G is made, and it is shown that is related to the weakly almost periodic compactification of the discretisation of G. Similar results are shown for the space of almost periodic functionals on M(G).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm204-3-2,
author = {Matthew Daws},
title = {Characterising weakly almost periodic functionals on the measure algebra},
journal = {Studia Mathematica},
volume = {204},
year = {2011},
pages = {213-234},
zbl = {1223.43005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm204-3-2}
}
Matthew Daws. Characterising weakly almost periodic functionals on the measure algebra. Studia Mathematica, Tome 204 (2011) pp. 213-234. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm204-3-2/