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

Tom 73 / 2006

Michael Skeide Banach Center Publications 73 (2006), 391-408 MSC: 46L08, 46L53, 46M05. DOI: 10.4064/bc73-0-31

Streszczenie

The category of von Neumann correspondences from $\mathcal B$ to $\mathcal C$ (or von Neumann ${\mathcal B}$-${\mathcal C}$modules) is dual to the category of von Neumann correspondences from $\mathcal C'$ to $\mathcal B'$ 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.

Autorzy

  • Michael SkeideDipartimento S.E.G.e S
    Università degli Studi del Molise
    Via de Sanctis
    86100 Campobasso, Italy
    e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek