## C*-algebras and their automorphism groups |

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C*-algebras and their automorphism groups

### Contents

Concrete CAlgebras | 19 |

Functionals and Representations | 41 |

Decomposition Theory | 91 |

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6 other sections not shown

### Common terms and phrases

a-system abelian elements abelian projection approximate unit assume automorphism Banach space belongs Borel algebra Borel field Borel function Borel isomorphic Borel set Borel space Borel structure bounded C*-dynamical system central projection closed ideal conclude cone Consequently contains continuous trace convergent convex COROLLARY corresponding covariant representation D-Borel decomposition define denote dense enveloping Borel algebra faithful normal finite G-invariant Glimm algebra Hausdorff space hereditary C*-subalgebra Hilbert space homomorphism implies irreducible representation isometry isomorphic LEMMA linear locally compact lower semi-continuous modular group monotone sequentially Moreover Neumann algebra non-zero normal morphism Notes and remarks null set obtain open set operator Polish space positive functional Proof PROPOSITION proved representation of G satisfies second countable separable C*-algebra sequence sequentially normal shows Sp(a spatially equivalent spectrum strongly subalgebra subspace surjective theorem theory topology uniformly continuous unique unit ball unitary representation weak weakly whence zero