No abstract

No abstract

According to J. Feldman and C. Moore's wellknown theorem on Cartan subalgebras, a variant of the group measure space construction gives an equivalence of categories between twisted countable standard measured equivalence relations and Cartan pairs, i.e., a von Neumann algebra (on a separable Hilbert space) together with a Cartan subalgebra. A. Kumjian gave a C * -algebraic analogue of this theorem in the early eighties. After a short survey of maximal abelian self-adjoint subalgebras in operator algebras, I present a natural definition of a Cartan subalgebra in a C * -algebra and an extension of Kumjian's theorem which covers graph algebras and some foliation algebras.

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.ABSTRACT. The C*-algebra 93 generated by the Wiener-Hopf operators defined over a subsemigroup of a locally compact group is shown to be the image of a groupoid C*-algebra under a suitable representation. When the subsemigroup is either a polyhedral cone or a homogeneous, self-dual cone in an Euclidean space, this representation may be used to show that j is postliminal and to find a composition series with very explicit subquotients. This yields a concrete parameterization of the spectrum of 1 and exhibits the topology on it.