Fundamentals of the Theory of Operator Algebras. Volume IIThis work and ""Fundamentals of the Theory of Operator Algebras, Volume I, Elementary Theory"" present an introduction to functional analysis and the initial fundamentals of $C^*$- and von Neumann algebra theory in a form suitable for both intermediate graduate courses and self-study. The authors provide a clear account of the introductory portions of this important and technically difficult subject. Major concepts are sometimes presented from several points of view; the account is leisurely when brevity would compromise clarity. An unusual feature in a text at this level is the extent to which it is self-contained; for example, it introduces all the elementary functional analysis needed. The emphasis is on teaching. Well supplied with exercises, the text assumes only basic measure theory and topology.The book presents the possibility for the design of numerous courses aimed at different audiences. '...these two volumes represent a magnificent achievement. They will be an essential item on every operator algebraist's bookshelves and will surely become the primary source of instruction for research students in von Neumann algebra theory' - ""Bulletin of the London Mathematical Society"". 'Volumes I and II were published in 1982 and 1983. Since then they have quickly established themselves as The Textbooks in operator algebra theory' - ""Bulletin of the American Mathematical Society"". 'One of the splendid features of the original two volumes is their large supply of exercises...which illustrate the results of the text and expand its scope' - ""L'Enseignement Mathematique"". |
Contents
| 385 | |
| 399 | |
Normal States and Unitary Equivalence | 454 |
The Trace | 504 |
Algebra and Commutant | 584 |
Special Representation of CAlgebras | 711 |
Tensor Products | 800 |
Approximation by Matrix Algebras | 889 |
Crossed Products | 936 |
Direct Integrals and Decompositions | 998 |
| 1049 | |
Other editions - View all
Fundamentals of the Theory of Operator Algebras, Volume 2 Richard V. Kadison,John R. Ringrose Limited preview - 1997 |
Common terms and phrases
A₁ abelian abelian projections abelian von Neumann acting on H automorphic representation automorphism group B₁ bounded linear C*-algebra C*-subalgebra central carrier central projection closure commutant convergent Corollary corresponding countably countably decomposable defined dense E₁ element everywhere Exercise F₁ factor of type faithful normal follows H₁ Hence Hilbert space Hint isomorphism L₂(R Lemma linear functional linear mapping linear span matrix units maximal abelian measurable minimal projections modular automorphism group Neumann algebra acting norm null set orthogonal family p₁ partial isometry polar decomposition positive linear Proof properly infinite Proposition prove R₁ range self-adjoint self-adjoint operator separable Hilbert space sequence Show space H strong-operator subalgebra subfactor subprojection subspace Suppose T₁ tensor product Theorem topology tracial weight type II₁ ultraweak ultraweakly continuous unique unit ball unit vector unitarily equivalent unitary operator von Neumann algebra weak-operator continuous x₁ π₁
Popular passages
Page 393 - Hausdorff spaces X and Y are homeomorphic if and only if C(X) and C(Y) are...
Page 1055 - M. Tomita, Standard forms of von Neumann algebras, Fifth Functional Analysis Symposium of the Math. Soc. of Japan, Sendai, 1967.