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

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.

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

References in corpus (3)

• Invariant means and finite representation theory of C*-algebras
• Lp-cohomology of symmetric spaces
• An l^{p}-Version of von Neumann Dimension for Representations of Equivalence Relations

Cited by in corpus (5)

• Polish Models and Sofic Entropy
• Sofic Entropy of Gaussian Actions
• An l^{p}-Version of von Neumann Dimension for Representations of Equivalence Relations
• Metric Mean Dimension for Algebraic Actions of Sofic Groups
• An l^{p}-Version of von Neumann Dimension for Banach Space Representation of Sofic Groups II