Characterising weakly almost periodic functionals on the measure algebra

• Autorzy: Matthew Daws
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 43A60: Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
• 46L89: Other ``noncommutative'' mathematics based on C * -algebra theory
• 43A20: L 1 -algebras on groups, semigroups, etc.
• 43A10: Measure algebras on groups, semigroups, etc.
• 81R50: Quantum groups and related algebraic methods
• 46G10: Vector-valued measures and integration

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 204
• Numer: 3
• Strony: 213-234

Daty

wydano

2011

Twórcy

autor

Matthew Daws

• School of Mathematics, University of Leeds, Leeds, LS2 9JT, United Kingdom

Identyfikatory

DOI

10.4064/sm204-3-2