Operator algebras

The theme of this symposium was operator algebras in a wide sense. In the last 40 years operator algebras has developed from a rather special dis- pline within functional analysis to become a central ? eld in mathematics often described as “non-commutative geometry” (see for example the book “Non-Commutative Geometry” by the Fields medalist Alain Connes). It has branched out in several sub-disciplines and made contact with other subjects like for example mathematical physics, algebraic topology, geometry, dyn- ical systems, knot theory, ergodic theory, wavelets, representations of groups and quantum groups. Norway has a relatively strong group of researchers in the subject, which contributed to the award of the ? rst symposium in the series of Abel Symposia to this group. The contributions to this volume give a state-of-the-art account of some of these sub-disciplines and the variety of topics re? ect to some extent how the subject has branched out. We are happy that some of the top researchers in the ? eld were willing to contribute. The basic ? eld of operator algebras is classi? ed within mathematics as part of functional analysis. Functional analysis treats analysis on in? nite - mensional spaces by using topological concepts. A linear map between two such spaces is called an operator. Examples are di? erential and integral - erators. An important feature is that the composition of two operators is a non-commutative operation.