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arXiv · 1110.5390

An l^{p}-Version of von-Neumann Dimension For Banach Space Representations of Sofic Groups

Ben Hayes
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Abstract

A. Gournay defined a notion of $l^{p}$-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.

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Ben Hayes. 2013-09-30. An l^{p}-Version of von-Neumann Dimension For Banach Space Representations of Sofic Groups. https://doi.org/10.1016/j.jfa.2013.09.014

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