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Let G be a compact abelian group, acting σ-weakly continuously as a group of 1-automorphisms α on a von Neumann algebra R. We give necessary and sufficient conditions for α to be inner, based on the structure of the lattice of projections in the center of the fixed-point algebra. As an application, we show that if α satisfies a spectrum condition with respect to a suitably chosen positive semigroup in the dual of G, then α is inner, and the implementing unitary representation can be chosen with positive spectrum.  相似文献   

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Summary Let Γ=〈g 1〉*〈g 2〉*...*〈g n 〉*... be a free product of cyclic groups with generators {g i }, andC r * (Γ, Λ) be the C*-algebra generated by the reduced group C*-algebraC r * Γ and a set of projectionsP gL associated with a subset Λ of {g i }. We prove the following: (1)C r * (Γ, Λ) is *-isomorphic to the reduced cross product for certain Hausdorff compact spaceX Λ constructed from Γ and its boundary ∂Γ. (2)C r * (Γ, Λ) is either a purely infinite, simple C*-algebra or an extension of a purely infinite, simple C*-altebra, depending on the pair (Γ, Λ). (3)C r * (Г, Λ) is nuclear if and only if the subgroup ΓΛ generated by {g i }/Λ is amenable. Partially supported by RMC grant 45/290/603 from the University of Newcastle Partially supported by NSF grant DMS-9225076 and a Taft travel grant from the University of Cincinnati  相似文献   

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Let K be a finite abelian group and let H be the holomorph of K. It is shown that every Coleman automorphism of H is an inner automorphism. As an immediate consequence of this result, it is obtained that the normalizer property holds for H.  相似文献   

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We prove that the automorphisms of any separable C*-algebra that does not have continuous trace are not classifiable by countable structures up to unitary equivalence. This implies a dichotomy for the Borel complexity of the relation of unitary equivalence of automorphisms of a separable unital C*-algebra: Such relation is either smooth or not even classifiable by countable structures.  相似文献   

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Mathematische Zeitschrift -  相似文献   

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We obtain two characterizations of the bi-inner Hopf *-automorphisms of a finite-dimensional Hopf C*-algebra, by means of an analysis of the structure of convolution products in this class of Hopf C*-algebra.  相似文献   

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Let G be the Banach-Lie group of all holomorphic automorphisms of the open unit ball in a J*-algebra of operators. Let be the family of all collectively compact subsets W contained in . We show that the subgroup FG of all those gG that preserve the family is a closed Lie subgroup of G and characterize its Banach-Lie algebra. We make a detailed study of F when is a Cartan factor.   相似文献   

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