On a class of smooth Frechet subalgebras of C * -algebras |
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Authors: | SUBHASH J BHATT DINESH J KARIA MEETAL M SHAH |
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Affiliation: | 1. Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar, Gujarat, 388 120, India
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Abstract: | 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 $ensuremath{{mathcal B}}$ of a C *-algebra as a noncommutative analogue of the algebra C ?∞?[a,b] of smooth functions. Regularity properties like spectral invariance, closure under functional calculi and domain invariance of homomorphisms are derived expressing $ensuremath{{mathcal B}}$ as an inverse limit over n of Banach $(D^*_n)$ -algebras. Several examples of such smooth algebras are exhibited. |
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