2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66189We 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.29 pages, to appear in J. Operator Theory. Some proofs from Section 6 have been rewritten to avoid an incorrect result in the literatureOperator Algebras46L52; 46L10text