A Note on Some Uniform Algebra Generated by Smooth Functions in the Plane
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...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/905650 |
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| _version_ | 1832552843303714816 |
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| author | Raymond Mortini Rudolf Rupp |
| author_facet | Raymond Mortini Rudolf Rupp |
| author_sort | Raymond Mortini |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3f64b6c2b0ed43d1863efa125ade3d72 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-3f64b6c2b0ed43d1863efa125ade3d722025-02-03T05:57:36ZengWileyJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/905650905650A Note on Some Uniform Algebra Generated by Smooth Functions in the PlaneRaymond Mortini0Rudolf Rupp1Département de Mathématiques, LMAM, UMR 7122, Université Paul Verlaine, Ile du Saulcy, 57045 Metz, FranceFakultät Allgemeinwissenschaften, Georg-Simon-Ohm-Hochschule Nürnberg, Keßlerplatz 12, 90489 Nürnberg, GermanyWe 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.http://dx.doi.org/10.1155/2012/905650 |
| spellingShingle | Raymond Mortini Rudolf Rupp A Note on Some Uniform Algebra Generated by Smooth Functions in the Plane Journal of Function Spaces and Applications |
| title | A Note on Some Uniform Algebra Generated by Smooth Functions in the Plane |
| title_full | A Note on Some Uniform Algebra Generated by Smooth Functions in the Plane |
| title_fullStr | A Note on Some Uniform Algebra Generated by Smooth Functions in the Plane |
| title_full_unstemmed | A Note on Some Uniform Algebra Generated by Smooth Functions in the Plane |
| title_short | A Note on Some Uniform Algebra Generated by Smooth Functions in the Plane |
| title_sort | note on some uniform algebra generated by smooth functions in the plane |
| url | http://dx.doi.org/10.1155/2012/905650 |
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