## Introduction to Operator AlgebrasThis book is an introductory text on one of the most important fields of Mathematics, the theory of operator algebras. It offers a readable exposition of the basic concepts, techniques, structures and important results of operator algebras. Written in a self-contained manner, with an emphasis on understanding, it serves as an ideal text for graduate students. |

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### Contents

Introduction | 1 |

Chapter 2 | 71 |

Chapter 3 | 163 |

Chapter 4 | 213 |

Chapter 5 | 237 |

The Classification of Von Neumann Algebras | 267 |

Chpater 7 | 313 |

Chpater 8 | 347 |

Chapter 11 | 426 |

Chapter 12 | 448 |

Chapter 13 | 490 |

Chapter 14 | 538 |

Chapter 15 | 570 |

Chapter 16 | 613 |

Chapter 17 | 682 |

Appendix | 714 |

### Common terms and phrases

a-finite abelian abelian projection algebra on H assume automorphism group Banach space Borel map Borel measure Borel space Borel subset bounded C*-algebra C*-norm C*-subalgebra Clearly closed subset closed two-sided ideal compact subset contradiction countable define denoted equivalent exists finite projection follows Further Hence Hilbert space irreducible isometry isomorphic Let G linear subspace maximal measurable field Moreover non-zero central projection non-zero projection nondegenerate norm open subset orthogonal family Pick polar decomposition Polish space positive linear functional projection from H Proof properly infinite purely infinite Q.E.D. Definition Q.E.D. Lemma Q.E.D. Proposition Q.E.D. Theorem regular Borel measure representation respectively semi-finite normal trace sequence space H spectral space strongly continuous subalgebra subfactor suffices to show supp Suppose topology trace on M+ uniquely extended unit ball unitary element unitary operator VN algebra xa G Zorn lemma

### References to this book

The Complete Dimension Theory of Partially Ordered Systems with ..., Issue 831 K. R. Goodearl,Friedrich Wehrung No preview available - 2005 |