Further Structure

Abstract

There is an important class of C^*-algebras called the Type I C^*-algebras, which can be characterized in several apparently different ways, which is precisely the class of C^*-algebras with “tractable” representation theory and which therefore has traditionally been regarded as the class of “reasonable” C^*-algebras whose structure can be “understood.” Although in recent years the structure theory of C^*-algebras has been largely divorced from representation theory and there is now a much larger class of C^*-algebras whose structure can be “understood” in the modern sense, Type I C^*-algebras are still very important; furthermore, the structure of Type I C^*-algebras can be rather precisely described, forming a model for the structure and classification of more general classes of C^*-algebras.