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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The crossed product of a $ C\sp{\ast} $-algebra by an endomorphism


Author: William L. Paschke
Journal: Proc. Amer. Math. Soc. 80 (1980), 113-118
MSC: Primary 46L05; Secondary 46L55
MathSciNet review: 574518
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Abstract: Let A be a unital, strongly amenable $ {C^ \ast }$-algebra, $ \sigma :A \to pAp$ a $ ^ \ast $-isomorphism (where p is a proper projection of A), and S an isometry such that $ Sx{S^ \ast } = \sigma (x)$ for all x in A. If A has no nontrivial $ \sigma $-invariant ideals, then $ {C^ \ast }(A,S)$ is simple. Furthermore, $ {C^\ast}(A,S)$ is isomorphic to a corner of the crossed product of $ A \otimes $ (compacts) by an automorphism.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0574518-2
PII: S 0002-9939(1980)0574518-2
Keywords: $ {C^ \ast }$-algebra, crossed product, simple
Article copyright: © Copyright 1980 American Mathematical Society