Subhash J Bhatt
Articles written in Proceedings – Mathematical Sciences
Volume 100 Issue 3 December 1990 pp 259-273
Köthe spaces and topological algebra with bases
Nuclear Köthe sequence space
Volume 101 Issue 3 December 1991 pp 149-167
Complete positivity, tensor products and C^{*}-nuclearity for inverse limits of C^{*}-algebras
Subhash J Bhatt Dinesh J Karia
The paper aims at developing a theory of nuclear (in the topological algebraic sense) pro-C^{*}-algebras (which are inverse limits of C^{*}-algebras) by investigating completely positive maps and tensor products. By using the structure of matrix algebras over a pro-C^{*}-algebra, it is shown that a unital continuous linear map between pro-C^{*}-algebras
Volume 116 Issue 2 May 2006 pp 161-173 Regular Articles
Given an
Volume 123 Issue 3 August 2013 pp 393-413
On a Class of Smooth Frechet Subalgebras of $C^\ast$-Algebras
Subhash J Bhatt Dinesh J Karia Meetal M Shah
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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