Noncommutative Lp modules
Abstract
We construct classes of von Neumann algebra modules by considering ``column sums" of noncommutative Lp spaces. Our abstract characterization is based on an Lp/2-valued inner product, thereby generalizing Hilbert C*-modules and representations on Hilbert space. While the (single) representation theory is similar to the L2 case, the concept of Lp bimodule (p not 2) turns out to be nearly trivial.
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