## 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 |

XXIX | 179 |

XXX | 181 |

XXXI | 182 |

XXXII | 188 |

XXXIII | 192 |

XXXIV | 203 |

XXXV | 220 |

XXXVI | 229 |

### Common terms and phrases

a-finite a-strongly abelian abelian C*-algebra abelian von Neumann Ah)m approximate identity assume Banach algebra Banach space Borel set C*-algebra C*-subalgebra center valued trace central projection closed ideal closure commutes completely positive conjugate space contains continuous function converges strongly countable cross-norm cyclic representation define denote direct sum enveloping von Neumann equivalent faithful semifinite normal finite dimensional follows Hilbert space homomorphism invariant involutive Banach algebra isomorphism lower semicontinuous maximal abelian minimal projection Neumann algebra nonzero projection norm operator algebras polar decomposition Polish space positive linear functional predual Proof Q.E.D. Corollary Q.E.D. Definition Q.E.D. Lemma Q.E.D. Proposition Q.E.D. Theorem resp respectively self-adjoint semifinite normal trace sequence Show Souslin spectrum subalgebra Suppose tensor product theory topology unit ball unital C*-algebra universal enveloping vector von Neumann algebra x,y e