Dual Algebras and A-Measures
Weak-star closures of Gleason parts in the spectrum of a function algebra are studied. These closures relate to the bidual algebra and turn out both closed and open subsets of a compact hyperstonean space. Moreover, weak-star closures of the corresponding bands of measures are reducing. Among the ap...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2014/364271 |
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| _version_ | 1850235316559937536 |
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| author | Marek Kosiek Krzysztof Rudol |
| author_facet | Marek Kosiek Krzysztof Rudol |
| author_sort | Marek Kosiek |
| collection | DOAJ |
| description | Weak-star closures of Gleason parts in the spectrum of a function algebra are studied. These closures relate to the bidual algebra and turn out both closed and open subsets of a compact hyperstonean space. Moreover, weak-star closures of the corresponding bands of measures are reducing. Among the applications we have a complete solution of an abstract version of the problem, whether the set of nonnegative A-measures (called also Henkin measures) is closed with respect to the absolute continuity. When applied to the classical case of analytic functions on a domain of holomorphy Ω⊂Cn, our approach
avoids the use of integral formulae for analytic functions, strict pseudoconvexity, or some other regularity of Ω. We also investigate the relation between the algebra of bounded holomorphic functions on Ω and its abstract counterpart—the w* closure of a function algebra A in the dual of the band of measures generated by one of Gleason parts of the spectrum of A. |
| format | Article |
| id | doaj-art-112ab0eaeca54165a43a189a8ea60b88 |
| institution | OA Journals |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-112ab0eaeca54165a43a189a8ea60b882025-08-20T02:02:19ZengWileyJournal of Function Spaces2314-88962314-88882014-01-01201410.1155/2014/364271364271Dual Algebras and A-MeasuresMarek Kosiek0Krzysztof Rudol1Faculty of Mathematics and Computer Sciences, Jagiellonian University, ulica Prof. St. Lojasiewicza 6, 30-348 Kraków, PolandFaculty of Applied Mathematics, AGH University of Science and Technology, Aleja Mickiewicza 30, 30-059 Kraków, PolandWeak-star closures of Gleason parts in the spectrum of a function algebra are studied. These closures relate to the bidual algebra and turn out both closed and open subsets of a compact hyperstonean space. Moreover, weak-star closures of the corresponding bands of measures are reducing. Among the applications we have a complete solution of an abstract version of the problem, whether the set of nonnegative A-measures (called also Henkin measures) is closed with respect to the absolute continuity. When applied to the classical case of analytic functions on a domain of holomorphy Ω⊂Cn, our approach avoids the use of integral formulae for analytic functions, strict pseudoconvexity, or some other regularity of Ω. We also investigate the relation between the algebra of bounded holomorphic functions on Ω and its abstract counterpart—the w* closure of a function algebra A in the dual of the band of measures generated by one of Gleason parts of the spectrum of A.http://dx.doi.org/10.1155/2014/364271 |
| spellingShingle | Marek Kosiek Krzysztof Rudol Dual Algebras and A-Measures Journal of Function Spaces |
| title | Dual Algebras and A-Measures |
| title_full | Dual Algebras and A-Measures |
| title_fullStr | Dual Algebras and A-Measures |
| title_full_unstemmed | Dual Algebras and A-Measures |
| title_short | Dual Algebras and A-Measures |
| title_sort | dual algebras and a measures |
| url | http://dx.doi.org/10.1155/2014/364271 |
| work_keys_str_mv | AT marekkosiek dualalgebrasandameasures AT krzysztofrudol dualalgebrasandameasures |