Enveloping Σ-C *-algebra of a smooth Frechet algebra crossed product by ℝ,K-theory and differential structure inC *-algebras |
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Authors: | Subhash J. Bhatt |
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Affiliation: | (1) Department of Mathematics, Sardar Patel University, 388 120 Vallabh Vidyanagar, India |
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Abstract: | 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. |
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Keywords: | Frechet*-algebra enveloping Σ -C *-algebra smooth crossed product m-tempered action K-theory differential structure inC *-algebras |
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