Enveloping Σ-C*-algebra of a smooth Frechet algebra crossed product by ℝ,K-theory and differential structure inC*-algebras
Given anm-tempered strongly continuous action α of ℝ by continuous*-automorphisms of a Frechet*-algebraA, it is shown that the enveloping ↡-C*-algebraE(S(ℝ, A∞, α)) of the smooth Schwartz crossed productS(ℝ,A∞, α) of the Frechet algebra A∞ of C∞-elements ofA is isomorphic to the Σ-C*-crossed productC*(ℝ,E(A), α) of the enveloping Σ-C*-algebraE(A) ofA by the induced action. WhenA is a hermitianQ-algebra, one getsK-theory isomorphismRK*(S(ℝ, A∞, α)) =K*(C*(ℝ,E(A), α) for the representableK-theory of Frechet algebras. An application to the differential structure of aC*-algebra defined by densely defined differential seminorms is given.
Volume 132, 2022
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