An l^{p}-Version of von-Neumann Dimension For Banach Space Representations of Sofic Groups
Functional Analysis
2014-04-03 v7 Operator Algebras
Abstract
A. Gournay defined a notion of -dimension for subspaces of the l^{q}-left-regular representation of an amenable discrete group. We give an alternative definition that works for sofic groups and a different notion for groups satisfying the Connes embedding conjecture, and for more general representations on Banach spaces. We extend certain results due to Gournay, as well as discuss l^{p}-Betti numbers of Free groups.
Keywords
Cite
@article{arxiv.1110.5390,
title = {An l^{p}-Version of von-Neumann Dimension For Banach Space Representations of Sofic Groups},
author = {Ben Hayes},
journal= {arXiv preprint arXiv:1110.5390},
year = {2014}
}
Comments
65 pages, 7 figures. This is the final version. To appear in Journal of Functional Analysis. Much of the old article has been added to arXiv:1302.2286 so as to make the two papers roughly the same length