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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