## C*-algebrasNormed involutive algebras -- Positive forms and representations -- Spectrum of a C*-algebra -- Liminal C*-Algebras -- Type of a representation -- Traces and representations -- Quasi-spectrum -- Integration and distintegration of representations -- C*-algebras of Type I -- Continuous fields of C*-Algebras -- Extension to C*-Algebras of Stone-Weierstrass theorem -- Enveloping Von Neumann algebra of a C*-Algebra -- Unitary representations of locally compact groups -- Square-integrable irreducible representations -- Representations of compact groups -- Almost-periodic functions -- Characters of a locally compact group -- Dual of a locally compact group. |

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### Contents

NORMED INVOLUTIVE ALGEBRAS | 3 |

POSITIVE FORMS AND REPRESENTATIONS | 26 |

THE SPECTRUM OF A CALGEBRA | 69 |

Copyright | |

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### Common terms and phrases

Acad Amer Anal associated automorphisms Banach spaces bounded Bull C*-algebra called canonical central character closed two-sided ideal commutative complete condition contained continuous field continuous unitary representation converges defined DEFINITION denote dense direct dual element equal equivalent exists extends fact factor representation finite finite-dimensional follows function hence hermitian Hilbert space identified identity invariant involutive algebra irreducible representations isomorphism LEMMA Let G Let H limit linear form locally compact group mapping Math maximal measure Moreover morphism neighbourhood Neumann algebra non-zero norm normal notation obtained operator operator algebras Phys positive forms postliminal Proc projection properties PROPOSITION prove pure References representation of G resp satisfied separable sequence square-integrable standard structure subset subspace Suppose theorem theory topology trace Trans transforms unique unital vanishes vector von Neumann algebra