% Encoding: UTF-8
@COMMENT{BibTeX export based on data in FAU CRIS: https://cris.fau.de/}
@COMMENT{For any questions please write to cris-support@fau.de}
@article{faucris.110209484,
abstract = {The construction of an infinite tensor product of the $C^*$-algebra $C{\_}0(\R)$ is not obvious, because it is nonunital, and it has no nonzero projection. Based on a choice of an approximate identity, we construct here an infinite tensor product of $C{\_}0(\R),$ denoted $\al L.\s{\al V.}.,$ and use it to find (partial) group algebras for the full continuous representation theory of $\R^{(\N)}.$ We obtain an interpretation of the Bochner--Minlos theorem in $\R^{(\N)}$ as the pure state space decomposition of the partial group algebras which generate $\al L.\s{\al V.}..$ We analyze the representation theory of $\al L.\s{\al V.}.,$ and show that there is a bijection between a natural set of representations of $\al L.\s{\al V.}.$ and ${\rm Rep} (\R^{(\N)},\al H. )\,,$ but that there is an extra part which essentially consists of the representation theory of a multiplicative semigroup $\al Q.$ which depends on the initial choice of approximate identity. },
author = {Grundling, Hendrik and Neeb, Karl-Hermann},
doi = {10.7900/jot.2011aug22.1930},
faupublication = {yes},
journal = {Journal of Operator Theory},
pages = {311 - 353},
peerreviewed = {Yes},
title = {{Infinite} {Tensor} {Products} of {Cā}({R}): {Towards} a {Group} {Algebra} for {R}ā},
volume = {70},
year = {2013}
}