By Kenneth R. Davidson
The topic of C*-algebras bought a dramatic revitalization within the Nineteen Seventies via the advent of topological equipment during the paintings of Brown, Douglas, and Fillmore on extensions of C*-algebras and Elliott's use of $K$-theory to supply an invaluable category of AF algebras. those effects have been the start of a wonderful new set of instruments for studying concrete C*-algebras.
This booklet is an introductory graduate point textual content which offers the fundamentals of the topic via an in depth research of a number of vital sessions of C*-algebras. the improvement of operator algebras within the final two decades has been according to a cautious learn of those specified sessions. whereas there are lots of books on C*-algebras and operator algebras on hand, this can be the 1st one to try to provide an explanation for the true examples that researchers use to check their hypotheses. issues comprise AF algebras, Bunce-Deddens and Cuntz algebras, the Toeplitz algebra, irrational rotation algebras, team C*-algebras, discrete crossed items, abelian C*-algebras (spectral idea and approximate unitary equivalence) and extensions. It additionally introduces many smooth innovations and leads to the topic comparable to actual rank 0 algebras, topological good rank, quasidiagonality, and numerous new structures.
These notes have been compiled throughout the author's participation within the specified yr on C*-algebras on the Fields Institute for examine in Mathematical Sciences through the 1994-1995 educational yr. the sphere of C*-algebras touches upon many different components of arithmetic similar to team representations, dynamical structures, physics, $K$-theory, and topology.
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