Journal ArticleDOI
States and automorphism groups of operator algebras
TLDR
In this article, it was shown that the discrete spectrum of an abelian unitary automorphism group acting as automorphisms of a von Neumann algebra is characterized by elements in the CAR algebra.Abstract:
Suppose that a group of automorphisms of a von Neumann algebraM, fixes the center elementwise We show that if this group commutes with the modular (KMS) automorphism group associated with a normal faithful state onM, then this state is left invariant by the group of automorphisms As a result we obtain a “noncommutative” ergodic theorem The discrete spectrum of an abelian unitary group acting as automorphisms ofM is completely characterized by elements inM We discuss the KMS condition on the CAR algebra with respect to quasi-free automorphisms and gauge invariant generalized free states We also obtain a necessary and sufficient condition for the CAR algebra and a quasi-free automorphism group to be η-abelianread more
Citations
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Conditional Expectations in von Neumann Algebras
TL;DR: In this article, it was shown that a von Neumann algebra M is invariant under modular automorphism group σtϑ associated with ϑ if and only if there exists a σ-weakly continuous faithful projection ϵ of norm one from M onto N such that ϑ(x) = ϑ ∘ ϵ(x), for every xϵMϑ.
Journal ArticleDOI
Properties of Quantum Markovian Master Equations
Vittorio Gorini,Alberto Frigerio,Maurizio Verri,Andrzej Kossakowski,E. C. G. Sudarshan,E. C. G. Sudarshan +5 more
TL;DR: In this paper, the authors give an essentially self-contained account of structural properties of quantum open Markovian systems and discuss a general form of quantum detailed balance and its relation to thermal relaxation and to microreversibility.
Journal ArticleDOI
Duality for crossed products and the structure of von Neumann algebras of type III
TL;DR: The structure of a v o n Neumann Neumann algebra of type I I I... ε I I ε, ε, ε is invariant to S ( ~ ) and T ( ~) of A. Connes.
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Conne’s bicentralizer problem and uniqueness of the injective factor of type III1
TL;DR: In this article, it was proved that injective factors of type III,t, 2. 1 on a separable Hilbert space are completely classified by their smooth flow of weights.
Journal ArticleDOI
The Radon-Nikodym theorem for von neumann algebras
TL;DR: In this article, a noncommutative Radon-Nikodym theorem was used to show that a von Neumann algebra is semi-finite if and only if it consists of inner automorphisms.
References
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Journal ArticleDOI
On the equilibrium states in quantum statistical mechanics
TL;DR: In this article, the authors studied the representation of the C*-algebra of observables corresponding to thermal equilibrium of a system at given temperature T and chemical potential μ and showed that the representation is reducible and that there exists a conjugation in the representation space, which maps the von Neumann algebra spanned by the representative of\(\mathfrak{A}\) onto its commutant.
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Free States of the Canonical Anticommutation Relations
Robert T. Powers,Erling Størmer +1 more
TL;DR: In this paper, it was shown that the cyclic representations induced by two gauge invariant generalized free states are quasi-equivalent if and only if the operators are of Hilbert-Schmidt class.