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

Alonso Delfín

doi:10.1007/s43037-025-00469-8

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

Functional Analysis 2025-11-24 v3 Operator Algebras

Authors: Alonso Delfín

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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.

Keywords

hilbert modules lp spaces and inequalities

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@article{arxiv.2410.10789,
  title  = {$L^p$-modules and $L^p$-correspondences},
  author = {Alonso Delfín},
  journal= {arXiv preprint arXiv:2410.10789},
  year   = {2025}
}

Comments

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

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

Abstract

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