Expectations in semifinite algebras

Semifinite Spectral Triples Associated with Graph C-algebras

We review the recent construction of semifinite spectral triples for graph C∗algebras. These examples have inspired many other developments and we review some of these such as the relation between the semifinite index and the Kasparov product, examples of noncommutative manifolds, and an index theorem in twisted cyclic theory using a KMS state. Alan L. Carey Mathematical Sciences Institute Aust...

Expectations in Von Neumann Algebras

Unbounded Conditional Expectations for Partial O∗-Algebras

Recommended by Ingo Witt The main purpose of this paper is to generalize studies of unbounded conditional expectations for O *-algebras to those for partial O *-algebras.

Conditional Expectations for Unbounded Operator Algebras

Two conditional expectations in unbounded operator algebras (O∗-algebras) are discussed. One is a vector conditional expectation defined by a linear map of an O∗-algebra into the Hilbert space on which the O∗-algebra acts. This has the usual properties of conditional expectations. This was defined by Gudder and Hudson. Another is an unbounded conditional expectation which is a positive linear m...

Representation of faithful normal expectations in von Neumann algebras