A Note on Some Uniform Algebra Generated by Smooth Functions in the Plane. (13th February 2012)

• Record Type: Journal Article
• Authors: Mortini, Raymond; Rupp, Rudolf
• Other Names: Kalton N. Academic Editor.
• Is Part Of: Journal of function spaces and applications. Volume 2012(2012)
• Publication Date: 2012-02-13
• Subjects: Function spaces -- Periodicals; 515.73
• DOI: 10.1155/2012/905650
• Languages: English
• ISSNs: 0972-6802

Abstract

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 K and holomorphic in the interior K ∘ of K . In this spirit, we also give elementary approaches to the calculation of these stable ranks for some classical function algebras on K .