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In previous work, we defined extended versions of von Neumann dimension forBanach space representations of sofic groups. The main application was adefinition of l^{p}-dimension and, using this, a proof that the actions of acountable 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 "Anl^{p}-Version of von Neumann Dimension for Banach Space Representation of SoficGroups." Tackling the case of finte-dimensional representations involvedpassing to equivalence relations. This is part of current research to beexplained in the paper "An l^{p}-Version of von Neumann Dimension forRepresentations of Equivalence Relations."

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