Mathematics – Operator Algebras
Scientific paper
2003-01-06
Mathematics
Operator Algebras
29 pages, to appear in J. Operator Theory. Some proofs from Section 6 have been rewritten to avoid an incorrect result in the
Scientific paper
We construct classes of von Neumann algebra modules by considering ``column sums" of noncommutative L^p spaces. Our abstract characterization is based on an L^{p/2}-valued inner product, thereby generalizing Hilbert C*-modules and representations on Hilbert space. While the (single) representation theory is similar to the L^2 case, the concept of L^p bimodule (p not 2) turns out to be nearly trivial.
Junge Marius
Sherman David
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