Commutants of von Neumann correspondences and duality of Eilenberg-Watts theorems by Rieffel and by Blecher

Michael Skeide

Banach Center Publications (2006)

  • Volume: 73, Issue: 1, page 391-408
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Michael Skeide. "Commutants of von Neumann correspondences and duality of Eilenberg-Watts theorems by Rieffel and by Blecher." Banach Center Publications 73.1 (2006): 391-408. <http://eudml.org/doc/281806>.

@article{MichaelSkeide2006,
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.},
author = {Michael Skeide},
journal = {Banach Center Publications},
language = {eng},
number = {1},
pages = {391-408},
title = {Commutants of von Neumann correspondences and duality of Eilenberg-Watts theorems by Rieffel and by Blecher},
url = {http://eudml.org/doc/281806},
volume = {73},
year = {2006},
}

TY - JOUR
AU - Michael Skeide
TI - Commutants of von Neumann correspondences and duality of Eilenberg-Watts theorems by Rieffel and by Blecher
JO - Banach Center Publications
PY - 2006
VL - 73
IS - 1
SP - 391
EP - 408
AB - 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.
LA - eng
UR - http://eudml.org/doc/281806
ER -

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