A Note on Some Uniform Algebra Generated by Smooth Functions in the Plane-Reference-Cited by-同舟云学术

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

Published:2012 Issue: Volume:2012 Page:1-15
ISSN:0972-6802
Container-title:Journal of Function Spaces and Applications
language:en
Short-container-title:Journal of Function Spaces and Applications

Author:

Mortini Raymond¹,Rupp Rudolf²

Affiliation:

1. Département de Mathématiques, LMAM, UMR 7122, Université Paul Verlaine, Ile du Saulcy, 57045 Metz, France

2. Fakultät Allgemeinwissenschaften, Georg-Simon-Ohm-Hochschule Nürnberg, Keßlerplatz 12, 90489 Nürnberg, Germany

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 .

Publisher

Hindawi Limited

Subject

Analysis

Link

http://downloads.hindawi.com/journals/jfs/2012/905650.pdf

Reference27 articles.

1. Stable range in Banach algebras

2. Stable rank in holomorphic function algebras

3. Extension problems and stable rank in commutative Banach algebras

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