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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-31,
author = {Michael Skeide},
title = {Commutants of von Neumann correspondences and duality of Eilenberg-Watts theorems by Rieffel and by Blecher},
journal = {Banach Center Publications},
volume = {72},
year = {2006},
pages = {391-408},
zbl = {1109.46050},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-31}
}
Michael Skeide. Commutants of von Neumann correspondences and duality of Eilenberg-Watts theorems by Rieffel and by Blecher. Banach Center Publications, Tome 72 (2006) pp. 391-408. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-31/