Proceedings of the International School of Physics "Enrico Fermi.", Volume 60N. Zanichelli, 1953 - Nuclear physics |
Contents
A VAN DAELE The TomitaTakesaki theory for von Neumann | 19 |
A CONNES The TomitaTakesaki theory and classification | 29 |
Invariant S group property computability and duality with | 37 |
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algebra of type ARAKI asymptotically Abelian automorphism group B₁ bounded C*-algebra closure Co-family commutant compact CONNES consider converges Corollary crossed product cyclic and separating decomposition defined Definition denote dense derivation domain dual equilibrium ergodic exists faithful normal finite statistics follows Gibbs condition Hence Hilbert space holomorphic hyperfinite implies infinite invariant inverse temperature isomorphism Journ KMS condition left inverse Lemma linear functional Math measure space modular automorphism morphism Neumann algebra norm one-parameter one-parameter group orthogonal P₁ P₂ partial isometry polar decomposition projection proof of Theorem Proposition prove Radon-Nikodym theorem representation satisfies self-adjoint operator separating vector sequence Spec g STØRMER strongly continuous subalgebra subset subspace TAKESAKI tensor product topology unique unit vector unitary von Neumann algebra weakly equivalent