Operator Algebras

Lawrence G. Brown and Gert K. Pedersen: Interpolation by Projections in C*-Algebras.- Alain Connes, Matilde Marcolli and Niranjan Ramachandran: KMS states and complex multiplication (Part II).- Joachim Cuntz: An algebraic description of boundary maps used in index theory.- Søren Eilers and Gunnar Restorff: On Rørdam's classification of certain C*-algebras with one non-trivial ideal.- George A. Elliott and Mikael Rørdam: Perturbation of Hausdorff moment sequences, and an application to the theory of C*-algebras of real rank zero.- David E. Evans: Twisted K-theory and Modular Invariants: I Quantum Doubles of Finite Groups.- Thierry Giordano, Ian F. Putnam and Christian F. Skau: The Orbit Structure of Cantor Minimal Z²-Systems.- Yoshikazu Katayama and Masamichi Takesaki: Outer Actions of a Group on a Factor.- Takeshi Katsura: Non-separable AF-algebras.- Eberhard Kirchberg: Central sequences in C*-algebras and strongly purely infinite algebras.- Akitaka Kishimoto: Lifting of an asymptotically inner flow for a separable C*-algebra.- Dimitri Shlyakhtenko: Remarks on Free Entropy Dimension.- Yoshimichi Ueda: Notes on Treeability and Costs for Discrete Groupoids in Operator Algebra Framework.- Index

The theme of the first Abel Symposium was operator algebras in a wide sense and this is the first volume in a prestigious new book series linked to the Abel prize. In the last 40 years operator algebras have developed from a rather special discipline within functional analysis to become a central field 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. The contributions to this volume give a state-of-the-art account of some of these sub-disciplines and the variety of topics reflect to some extent how the subject developed. Norway has a relatively strong group of researchers in the subject, which contributed to the award of the first symposium in the series of Abel Symposia to this group.