Algebry operatorów i ich zastosowania w fizyce

The Haagerup approximation property for a von Neumann algebra with a fixed faithful tracial state was introduced over 30 years ago by Marie Choda, who was motivated by the Haagerup property for discrete groups (which was then 4 years old). Recent study of the latter property in the world of quantum groups led naturally to the introduction of the Haagerup property for a von Neumann algebra with a fixed normal faithful semifinite weight. We will describe the latter, show that it does not depend on the choice of the weight and present some further equivalences. Based on joint work with Martijn Caspers (and also Rui Okayasu and Reiji Tomatsu).