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arXiv · 1302.2286

An l^{p}-Version of von Neumann Dimension for Banach Space Representation of Sofic Groups II

Ben Hayes
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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."

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Ben Hayes. 2013-02-10. An l^{p}-Version of von Neumann Dimension for Banach Space Representation of Sofic Groups II. https://doi.org/10.1016/j.jfa.2015.07.013

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