Functoriality of group algebras acting on $L^p$spaces
Abstract
We continue our study of group algebras acting on $L^p$spaces, particularly of algebras of $p$pseudofunctions of locally compact groups. We focus on the functoriality properties of these objects. We show that $p$pseudofunctions are functorial with respect to homomorphisms that are either injective, or whose kernel is amenable and has finite index. We also show that the universal completion of the group algebra with respect to representations on $L^p$spaces, is functorial with respect to quotient maps. As an application, we show that the algebras of $p$ and $q$pseudofunctions on $\mathbb{Z}$ are (abstractly) isometrically isomorphic as Banach algebras if and only if $p$ and $q$ are either equal or conjugate.
 Publication:

arXiv eprints
 Pub Date:
 August 2014
 arXiv:
 arXiv:1408.6137
 Bibcode:
 2014arXiv1408.6137G
 Keywords:

 Mathematics  Functional Analysis;
 Mathematics  Operator Algebras;
 Primary: 22D20;
 43A15. Secondary: 43A65;
 46E30
 EPrint:
 12 pages