Operator Algebras and Quantum Statistical Mechanics: C*- and W*-algebras, symmetry groups, decomposition of states |
Contents
Models of Quantum Statistical Mechanics 239 | 11 |
CAlgebras and von Neumann Algebras | 13 |
1 | 19 |
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A₁ abelian von Neumann analytic elements assume B₁ Banach space barycenter Borel Borel set bounded operators C*-algebra C*-algebra with identity characterization closed closure Co-semigroup commutant conditions are equivalent cone converges convex convex combination Corollary corresponding deduces defined Definition denote dense derivation dual ergodic establishes example exists F)-continuous factor finite following conditions G-abelian G-ergodic G-invariant group of automorphisms hence Hilbert space implies invariant invertible irreducible isometry isomorphism LC(H Lemma linear functional locally compact Math maximal measure Moreover morphism Neumann algebra norm normal o-weakly one-parameter group operator algebras orthogonal measures polar decomposition projection Proposition prove quasi-local algebra remark result satisfies Section selfadjoint semigroup space H spectral spectrum strongly continuous subset subspace symmetry theory topology U₁ uniformly unique unitary operators vector von Neumann algebra w₁ w₂ weakly ΑΩ