• Meetal M Shah

      Articles written in Proceedings – Mathematical Sciences

    • On a Class of Smooth Frechet Subalgebras of $C^\ast$-Algebras

      Subhash J Bhatt Dinesh J Karia Meetal M Shah

      More Details Abstract Fulltext PDF

      The paper contributes to understanding the differential structure in a $C^∗$-algebra. Refining the Banach $(D^∗_p)$-algebras investigated by Kissin and Shulman as noncommutative analogues of the algebra $C^p[a,b]$ of 𝑝-times continuously differentiable functions, we investigate a Frechet $(D^∗\infty)$-subalgebra $\mathcal{B}$ of a $C^∗$-algebra as a noncommutative analogue of the algebra $C^\infty[a,b]$ of smooth functions. Regularity properties like spectral invariance, closure under functional calculi and domain invariance of homomorphisms are derived expressing $\mathcal{B}$ as an inverse limit over 𝑛 of Banach $(D^∗_n)$-algebras. Several examples of such smooth algebras are exhibited.

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