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 (I) Elementary Theory and (II) Advanced Theory; the latter two volumes, published in 1991 and 1992, present complete solutions to the exercises in volumes I and II.
Chapter 1. Linear spaces
Chapter 2. Basics of Hilbert Space and Linear Operators
Chapter 3. Banach Algebras
Chapter 4. Elementary C*-Algebra Theory
Chapter 5. Elementary von Neumann Algebra Theory
Chapter 6. Comparison Theory of Projection
Chapter 7. Normal States and Unitary Equivalence of von Neumann Algebras
Chapter 8. The Trace
Chapter 9. Algebra and Commutant
Chapter 10. Special Representation of C*-Algebras
Chapter 11. Tensor Products
Chapter 12. Approximation by Matrix Algebras
Chapter 13. Crossed Products
Chapter 14. Direct Integrals and Decompositions
Volumes III and IV follow Volumes I and II chapter-by-chapter with solutions to the exercises.
According to Nick Lord (writing for The Mathematical Gazette), 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.[1] Ringrose and Kadison wrote with a pedagogical goal in mind, purposefully keeping the references sparse and including a long list of exercises.[2] 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: