Proceedings of the International School of Physics "Enrico Fermi.", Volume 60N. Zanichelli, 1953 - Nuclear physics |
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Page 56
... dual weight of q . ( 3.8 ) Roughly speaking , the dual weight is given by the formula ğ ( x ) = p ( x ( 0 ) ) for a good » element x of R ( M ; a ) of the form x = = fx ( x ( g ) ) λ ( g ) dy . The associated modular authomorphism group ...
... dual weight of q . ( 3.8 ) Roughly speaking , the dual weight is given by the formula ğ ( x ) = p ( x ( 0 ) ) for a good » element x of R ( M ; a ) of the form x = = fx ( x ( g ) ) λ ( g ) dy . The associated modular authomorphism group ...
Page 57
... dual action â . We can extend the above result to more general fixed - points subalgebras . Namely , the following ... dual group of R is the additive group R itself . We denote by { 0 } the dual action of R on R ( M ; x ) . Suppose y is ...
... dual action â . We can extend the above result to more general fixed - points subalgebras . Namely , the following ... dual group of R is the additive group R itself . We denote by { 0 } the dual action of R on R ( M ; x ) . Suppose y is ...
Page 59
... dual weight Ф is the action of R dual to the action 0 on N. Hence N is the centralizer of the dual weight q . = The proof is a straightforward application of the results of Sect . 3 . — 53. Corollary . Under the same assumption as in ...
... dual weight Ф is the action of R dual to the action 0 on N. Hence N is the centralizer of the dual weight q . = The proof is a straightforward application of the results of Sect . 3 . — 53. Corollary . Under the same assumption as in ...
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