Wydawnictwa / Banach Center Publications / Wszystkie tomy

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.