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Commutants of von Neumann Correspondences and Duality of Eilenberg-Watts Theorems by Rieffel and by Blecher

M. Skeide
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Abstract

The category of von Neumann correspondences from B to C (or von Neumann B-C-modules) is dual to the category of von Neumann correspondences from C' to B' via a functor that generalizes naturally the functor that sends a von Neumann algebra to its commutant and back. We show that under this duality, called commutant, Rieffel's Eilenberg-Watts theorem (on functors between the categories of representations of two von Neumann algebras) switches into Blecher's Eilenberg-Watts theorem (on functors between the categories of von Neumann modules over two von Neumann algebras) and back.

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M. Skeide. 2005-02-11. Commutants of von Neumann Correspondences and Duality of Eilenberg-Watts Theorems by Rieffel and by Blecher. https://arxiv.org/abs/math/0502241

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