C*-algebras and Their Automorphism Groups

a-system abelian elements approximate unit assume automorphism Banach Banach space Borel algebra Borel set Borel structure bounded C*-algebra C*-dynamical system central projection closed ideal closure commutative conclude Consequently contains convergent convex COROLLARY countable cyclic D-Borel define denote dense du(t dµ(t faithful normal finite follows G-invariant Glimm algebra H₁ Hausdorff space Hilbert space homomorphism implies irreducible representation isometry isomorphic L²(G LEMMA linear locally compact lower semi-continuous maximal measure Mm(n modular group Moreover Neumann algebra non-zero norm normal morphism Notes and remarks operator orthogonal P₁ Polish space positive functional Proof PROPOSITION representation of G satisfies semi-finite separable C*-algebra sequence sequentially normal Sp(a Sp(x spectral spectrum subalgebra subset subspace theorem theory topology unique unit ball unitary representation vector von Neumann algebra weak weakly whence