Enveloping $σ$-$C^*$-algebra of a smooth Frechet algebra crossed product by $R$, $K$-theory and differential structure in $C^*$-algebras

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dc.creatorBhatt, Subhash J
dc.date2006-07-27
dc.date.accessioned2026-07-07T07:21:02Z
dc.date.available2026-07-07T07:21:02Z
dc.descriptionGiven an $m$-tempered strongly continuous action $α$ of $\R$ by continuous $^{*}$-automorphisms of a Frechet $^{*}$-algebra $A$, it is shown that the enveloping \hbox{$σ$-$C^{*}$-algebra} $E(S(\R,A^{\infty},α))$ of the smooth Schwartz crossed product $S(\R,A^{\infty},α)$ of the Frechet algebra $A^{\infty}$ of $C^{\infty}$-elements of $A$ is isomorphic to the \hbox{$σ$-$C^{*}$-crossed} product $C^{*}(\R,E(A),α)$ of the enveloping $σ$-$C^{*}$-algebra $E(A)$ of $A$ by the induced action. When $A$ is a hermitian $Q$-algebra, one gets $K$-theory isomorphism $RK_{*}(S(\R,A^{\infty},α)) = K_{*}(C^{*}(\R,E(A),α)$ for the representable $K$-theory of Frechet algebras. An application to the differential structure of a $C^{*}$-algebra defined by densely defined differential seminorms is given.
dc.description13 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/math/0607701
dc.identifierhttp://arxiv.org/abs/math/0607701
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115159
dc.subjectOperator Algebras
dc.subject46K99, 46L55, 46L80, 46H35
dc.titleEnveloping $σ$-$C^*$-algebra of a smooth Frechet algebra crossed product by $R$, $K$-theory and differential structure in $C^*$-algebras
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