## Theory of Operator Algebras ISince its inception by von Neumann 70 years ago, the theory of operator algebras has become a rapidly developing area of importance for the understanding of many areas of mathematics and theoretical physics. Accessible to the non-specialist, this first part of a three-volume treatise provides a clear, carefully written survey that emphasizes the theory's analytical and topological aspects. |

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### Contents

II | 1 |

III | 2 |

IV | 6 |

V | 13 |

VI | 17 |

VII | 21 |

VIII | 23 |

IX | 25 |

XXXI | 179 |

XXXII | 181 |

XXXIV | 182 |

XXXV | 188 |

XXXVI | 192 |

XXXVII | 203 |

XXXVIII | 220 |

XXXIX | 229 |

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### Common terms and phrases

abelian admits approximate assertion assume Banach algebra Banach space belongs bounded C*-algebra called central projection choose closed closure commutes compact completely condition consider contains continuous function converges convex Corollary corresponding countable cyclic decomposition define Definition denote dense direct element equivalent exists extended fact factor faithful field finite fixed follows given Hence Hilbert space ideal identified identity implies increasing induced inequality infinite integral invariant isometry isomorphism Lemma locally maximal means measure Neumann algebra nonzero norm normal normal trace o-finite o-weakly obtain operator orthogonal positive positive linear functional projection PROOF Proposition prove representation resp respectively restriction self-adjoint semifinite separable sequence Show space H spectrum strongly structure subset subspace Suppose tensor product Theorem theory topology unique unit ball unitary universal valued vector