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

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

2011-10-25

arxiv.org/abs/1110.5390v6

Mathematics

Functional Analysis

65 pages, 7 figures. Corrected some confusing typographical errors. I am very thankful to Hanfeng Li for pointing these out. T

Scientific paper

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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