# Characterising weakly almost periodic functionals on the measure algebra

Studia Mathematica (2011)

- Volume: 204, Issue: 3, page 213-234
- ISSN: 0039-3223

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topMatthew Daws. "Characterising weakly almost periodic functionals on the measure algebra." Studia Mathematica 204.3 (2011): 213-234. <http://eudml.org/doc/285611>.

@article{MatthewDaws2011,

abstract = {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).},

author = {Matthew Daws},

journal = {Studia Mathematica},

keywords = {measure algebra; almost periodic; weakly almost periodic},

language = {eng},

number = {3},

pages = {213-234},

title = {Characterising weakly almost periodic functionals on the measure algebra},

url = {http://eudml.org/doc/285611},

volume = {204},

year = {2011},

}

TY - JOUR

AU - Matthew Daws

TI - Characterising weakly almost periodic functionals on the measure algebra

JO - Studia Mathematica

PY - 2011

VL - 204

IS - 3

SP - 213

EP - 234

AB - 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).

LA - eng

KW - measure algebra; almost periodic; weakly almost periodic

UR - http://eudml.org/doc/285611

ER -

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