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Models of Quantum Statistical Mechanics 239
Notes and Remarks
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abelian action analysis analytic applications argument associated assume automorphisms Banach Banach space Borel bounded C*-algebra called characterization closed closure commutant compact concludes condition conditions are equivalent cone consider construction contains continuous converges convex Corollary corresponding cyclic decomposition deduces defined Definition denote dense derivation discussion dual elements ergodic establishes examine example exists extension fact factor Finally finite following conditions follows function given gives hence Hilbert space identity implies integral introduce invariant isomorphism Lemma limit linear locally Math maximal mean measure Moreover natural Neumann algebra norm normal o-weakly observables obtained operator orthogonal measures pair particular positive projection PROOF Proposition prove relation remark representation result satisfies selfadjoint semigroup separating sequence spectral spectrum statement strongly structure subalgebra subset symmetry Theorem theory topology uniformly unique unit unitary vector weak weakly