Fundamentals of the Theory of Operator Algebras


Fundamentals of the Theory of Operator Algebras is a four-volume textbook on the classical theory of operator algebras written by Richard Kadison and John Ringrose. The first two volumes, published in 1983 and 1986, are entitled Elementary Theory and Advanced Theory; the latter two volumes, published in 1991 and 1992, present complete solutions to the exercises in volumes I and II.

Contents

  • Volume I: Elementary Theory
  • Volume II: Advanced Theory
Volumes III and IV follow Volumes I and II chapter-by-chapter with solutions to the exercises.

Reception

According to Nick Lord, the two volumes "met with immediate acclaim from functional analysts as a clear, careful, self-contained introduction to C*- and von Neumann algebra theory", something many in the field felt was missing. Ringrose and Kadison wrote with a pedagogical goal in mind, purposefully keeping the references sparse and including a long list of exercises. These exercises have been described as "outstanding" and the solutions, in the later volumes, have been similarly commended. They wrote of their textbook that:
Gert K. Pederson wrote in 1994 of the volumes' popularity: