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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Representable $K$-theory of smooth crossed products by $\textbf {R}$ and $\textbf {Z}$


Authors: N. Christopher Phillips and Larry B. Schweitzer
Journal: Trans. Amer. Math. Soc. 344 (1994), 173-201
MSC: Primary 46L80; Secondary 19K99, 46H99, 46L87, 46M20
DOI: https://doi.org/10.1090/S0002-9947-1994-1219733-4
MathSciNet review: 1219733
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Abstract: We show that the Thorn isomorphism and the Pimsner-Voiculescu exact sequence both hold for smooth crossed products of Fréchet algebras by $\mathbb {R}$ and $\mathbb {Z}$ respectively. We also obtain the same results for ${L^1}$-crossed products of Banach algebras by $\mathbb {R}$ and $\mathbb {Z}$.


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Keywords: <I>m</I>-convex Fr&#233;chet algebra, smooth crossed product, representable <I>K</I>-theory, <I>m</I>-tempered action
Article copyright: © Copyright 1994 American Mathematical Society