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A Note on Some Uniform Algebra Generated by Smooth Functions in the Plane

DOI: 10.1155/2012/905650

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Abstract:

We determine, via classroom proofs, the maximal ideal space, the Bass stable rank as well as the topological and dense stable rank of the uniform closure of all complex-valued functions continuously differentiable on neighborhoods of a compact planar set and holomorphic in the interior ° of . In this spirit, we also give elementary approaches to the calculation of these stable ranks for some classical function algebras on .

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