Journal of Operator Theory

Volume 53, Issue 1, Winter 2005 pp. 3-34.

Noncommutative

$L^p$ modules

Authors: Marius Junge (1) and David Sherman (2)
Author institution: (1) Department of Mathematics, University of Illinois, Urbana, IL 61801, USA
(2) Department of Mathematics, University of California, Santa Barbara, CA 93106, USA

Summary: 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 (

$p \ne 2$ ) turns out to be nearly trivial.

Contents Full-Text PDF