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## Studia Mathematica

2011 | 204 | 3 | 213-234
Tytuł artykułu

### Characterising weakly almost periodic functionals on the measure algebra

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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 $K_{WAP}$. In this paper, we investigate properties of $K_{WAP}$. We present a short proof that $K_{WAP}$ 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 $K_{WAP}$ is related to G is made, and it is shown that $K_{WAP}$ 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).
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Tom
Numer
Strony
213-234
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Daty
wydano
2011
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autor
• School of Mathematics, University of Leeds, Leeds, LS2 9JT, United Kingdom
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