An l^{p}-Version of von Neumann Dimension for Banach Space Representation of Sofic Groups II
Abstract
In previous work, we defined extended versions of von Neumann dimension for Banach space representations of sofic groups. The main application was a definition of l^{p}-dimension and, using this, a proof that the actions of a countable discrete group G on l^{p}(G)^{oplus n} are pairwise non-isomorphic. We answer most of the Conjectures stated at the end of the previous paper "An l^{p}-Version of von Neumann Dimension for Banach Space Representation of Sofic Groups." Tackling the case of finte-dimensional representations involved passing to equivalence relations. This is part of current research to be explained in the paper "An l^{p}-Version of von Neumann Dimension for Representations of Equivalence Relations."
Keywords
Cite
@article{arxiv.1302.2286,
title = {An l^{p}-Version of von Neumann Dimension for Banach Space Representation of Sofic Groups II},
author = {Ben Hayes},
journal= {arXiv preprint arXiv:1302.2286},
year = {2015}
}
Comments
47 pages, Follow up paper to An l^{p}-Version of von Neumann Dimension for Banach Space Representation of Sofic Groups. Many changes, notably many typographical errors have been fixed, details have been added to Proposition 5.6 and new material has been added to Section 3. Accepted to Journal of Functional Analysis