## Fundamentals of the Theory of Operator Algebras. Volume IIFrom the reviews for Volumes I and II: ... 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 This book is extremely clear and well written and ideally suited for an introductory course on the subject or for a student who wishes to learn the fundamentals of the classical theory of operator algebras. --Zentralblatt MATH This work and Fundamentals of the Theory of Operator Algebras. Volume I, Elementary Theory (Graduate Studies in Mathematics, Volume 15) 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. |

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### 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 IV Richard V. Kadison, John R. Ringrose Limited preview - 1998 |

### Common terms and phrases

Accordingly acting applies argument assert assume automorphism Borel bounded C*-algebra choose closed closure commutant compact complete condition consider consists construction contains convergent Corollary corresponding countably cyclic decomposable decomposition Deduce defined Definition denote dense described direct discussion element equation equivalent everywhere example Exercise extends factor factor of type finite follows given Hence Hilbert space Hint ideal implemented integer irreducible isomorphism Lemma limit linear functional matricial matrix measurable modular Moreover multiplication non-zero norm notation Note null obtain orthogonal family paragraph partial isometry positive preceding projection Proof properties Proposition prove pure range relative Remark representation respectively restriction result satisfies self-adjoint semi-finite separating sequence Show space H strong-operator subalgebra subprojection subset suffices Suppose tensor product Theorem topology trace tracial ultraweakly continuous unique unit vector unitarily unitary operator vector von Neumann algebra weak weak-operator weight

### 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.