INJECTIVE ENVELOPES OF {C^ * }-DYNAMICAL SYSTEMS

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概要

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• The injective envelope I(A) of a {C^ * }-algebra A is a unique minimal injective {C^ * }-algebra containing A. As a dynamical system version of the injective envelope of a {C^ * }-algebra we show that for a {C^ * }-dynamical system (A, G, β) with G discrete there is a unique maximal {C^ * }-dynamical system (B, G, β) "containing" (A, G, α) so that A × <SUB>α r</SUB>G \subset B × <SUB>β r</SUB>G \subset I(A × <SUB>α r</SUB>G), where A × <SUB>α r</SUB>G is the reduced {C^ * }-crossed product of A by G. As applications we investigate the relationship between the original action α on A and its unique extension I(α) to I(A). In particular, a *-automorphism α of A is quasi-inner in the sense of Kishimoto if and only if I(α) is inner.

• 東北大学大学院理学研究科数学専攻の論文

著者

• HAMANA Masamichi

  Department of Mathematics Faculty of Education Toyama University

関連論文

• Regular embeddings of C*-algebras in monotone complete C*-algebras
• Injective Envelopes of Operator Systems
• Triple envelopes and Šilov boundaries of operator spaces
• EXTENSIONS OF DERIVATIONS AND AUTOMORPHISMS FROM {C^ * }-ALGEBRAS TO THEIR INJECTIVE ENVELOPES
• INJECTIVE ENVELOPES OF {C^ * }-DYNAMICAL SYSTEMS
• Tensor products for monotone complete C*-algebras, II

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