$L^p$-modules and $L^p$-correspondences

Abstract

We introduce an $L^p$-operator algebraic analogue of Hilbert C*- modules. We present the theory of concrete $L^p$-modules, their morphisms, and basic constructions including countable direct sums and tensor products. We then define $L^p$-correspondences and the interior tensor product of these.

AMSLaTeX; 20 pages. V3: Final version to appear in the Banach Journal of Mathematical Analysis. V2: Original paper has been rewritten and has been broken into two separate projects. This part now deals uniquely with the L^p-modules theory. The p-Cuntz-Pimsner part is being extended and is work currently in preparation