Functorial properties of weakly almost periodic functionals on the measure algebra
نویسنده
چکیده
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. In this paper, we investigate properties of K. We present two proofs, one using tensor product techniques, and the other using vector-valued integration, to show that K can naturally be turned into a semigroup whose product is separately continuous. This is in complete agreement with the classical situation when G is discrete. A study of how K is related to G is made, and it is shown that K 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). Subject classification: 43A10, 46L89, 46G10 (Primary); 43A20, 43A60, 81R50 (Secondary).
منابع مشابه
Weakly almost periodic functionals on the measure algebra
It is shown that the collection of weakly almost periodic functionals on the convolution algebra of a commutative Hopf von Neumann algebra is a C∗-algebra. This implies that the weakly almost periodic functionals on M(G), the measure algebra of a locally compact group G, is a C∗-subalgebra of M(G)∗ = C0(G) ∗∗. The proof builds upon a factorisation result, due to Young and Kaiser, for weakly com...
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