Characterising weakly almost periodic functionals on the measure algebra

Matthew 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 -