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

• Autorzy: Michael Skeide
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46L53: Noncommutative probability and statistics
• 46L08: C * -modules
• 46M05: Tensor products

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2006
• Tom: 73
• Numer: 1
• Strony: 391-408

Daty

wydano

2006

Twórcy

autor

Michael Skeide

• Dipartimento S.E.G.e S, Università degli Studi del Molise, Via de Sanctis, 86100 Campobasso, Italy

Identyfikatory

DOI

10.4064/bc73-0-31