A characterization of the algebra of holomorphic functions on a simply connected domain
Let A be a singly-generated ℱ-algebra. It is shown that A isomorphic to H(Ω) where Ω is a simply connected domain in ℂ if and only if A has no topological divisors of zero. It follows from this that there are exactly three ℱ-algebras (up to isomorphism) which are singly generated and have no topolog...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1989-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171289000086 |
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| _version_ | 1832550639090008064 |
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| author | Derming Wang Saleem Watson |
| author_facet | Derming Wang Saleem Watson |
| author_sort | Derming Wang |
| collection | DOAJ |
| description | Let A be a singly-generated ℱ-algebra. It is shown that A isomorphic to H(Ω)
where Ω is a simply connected domain in ℂ if and only if A has no topological divisors of
zero. It follows from this that there are exactly three ℱ-algebras (up to isomorphism) which
are singly generated and have no topological divisors of zero. |
| format | Article |
| id | doaj-art-8bb9460952bc40baa29d224dcd2ff1b1 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1989-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8bb9460952bc40baa29d224dcd2ff1b12025-02-03T06:06:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251989-01-01121656810.1155/S0161171289000086A characterization of the algebra of holomorphic functions on a simply connected domainDerming Wang0Saleem Watson1Department of Mathematics and Computer Science, California State University, Long Beach 90840, California, USADepartment of Mathematics and Computer Science, California State University, Long Beach 90840, California, USALet A be a singly-generated ℱ-algebra. It is shown that A isomorphic to H(Ω) where Ω is a simply connected domain in ℂ if and only if A has no topological divisors of zero. It follows from this that there are exactly three ℱ-algebras (up to isomorphism) which are singly generated and have no topological divisors of zero.http://dx.doi.org/10.1155/S0161171289000086 |
| spellingShingle | Derming Wang Saleem Watson A characterization of the algebra of holomorphic functions on a simply connected domain International Journal of Mathematics and Mathematical Sciences |
| title | A characterization of the algebra of holomorphic functions on a simply connected domain |
| title_full | A characterization of the algebra of holomorphic functions on a simply connected domain |
| title_fullStr | A characterization of the algebra of holomorphic functions on a simply connected domain |
| title_full_unstemmed | A characterization of the algebra of holomorphic functions on a simply connected domain |
| title_short | A characterization of the algebra of holomorphic functions on a simply connected domain |
| title_sort | characterization of the algebra of holomorphic functions on a simply connected domain |
| url | http://dx.doi.org/10.1155/S0161171289000086 |
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