## Theory of operator algebras I, Volume 1 |

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### Contents

Spectrum and Functional Calculus | 6 |

Gelfand Representation of Abelian Banach Algebras | 13 |

Continuity of Homomorphisms | 21 |

Copyright | |

27 other sections not shown

### Common terms and phrases

a-finite abelian 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 convex 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 locally compact space lower semicontinuous Math maximal abelian minimal projection Neumann algebra nonzero projection norm 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 topology unique unit ball unital C*-algebra universal enveloping vector x,y e