On functional representation of locally m-pseudoconvex algebras
Functional representation of a topological algebra (A,T) has been studied in many papers under various assumptions for the topology T on A. Usually the image Aˆ of the Gelfand map has been equipped with the compact-open topology. This leads, in several cases, to such kind of difficulties as, for ins...
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| Format: | Article |
| Language: | English |
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Wiley
1999-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171299222235 |
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| _version_ | 1832564567893344256 |
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| author | Jorma Arhippainen |
| author_facet | Jorma Arhippainen |
| author_sort | Jorma Arhippainen |
| collection | DOAJ |
| description | Functional representation of a topological algebra (A,T) has been studied in many papers under various assumptions for the
topology T on A. Usually the image Aˆ of the Gelfand map has been equipped with the compact-open topology. This leads, in several cases, to such kind of difficulties as, for instance,
that the Gelfand map is not necessarily continuous or that the compact-open topology is not of the same type as the topology T. In this paper, we study locally m-pseudoconvex algebras and provide Aˆ with such kind of topology that the above two claims are fulfilled. By using this representation the description of the closed ideals of (A,T) is studied. |
| format | Article |
| id | doaj-art-c658b3d94fe0473b89318d7937ba88c8 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1999-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-c658b3d94fe0473b89318d7937ba88c82025-02-03T01:10:44ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251999-01-0122222323710.1155/S0161171299222235On functional representation of locally m-pseudoconvex algebrasJorma Arhippainen0Department of Mathematical Sciences, University of Oulu, P.O. Box 400, Oulu SF-90570, FinlandFunctional representation of a topological algebra (A,T) has been studied in many papers under various assumptions for the topology T on A. Usually the image Aˆ of the Gelfand map has been equipped with the compact-open topology. This leads, in several cases, to such kind of difficulties as, for instance, that the Gelfand map is not necessarily continuous or that the compact-open topology is not of the same type as the topology T. In this paper, we study locally m-pseudoconvex algebras and provide Aˆ with such kind of topology that the above two claims are fulfilled. By using this representation the description of the closed ideals of (A,T) is studied.http://dx.doi.org/10.1155/S0161171299222235Locally m-pseudoconvex algebrasclosed idealsGelfand representation. |
| spellingShingle | Jorma Arhippainen On functional representation of locally m-pseudoconvex algebras International Journal of Mathematics and Mathematical Sciences Locally m-pseudoconvex algebras closed ideals Gelfand representation. |
| title | On functional representation
of locally m-pseudoconvex algebras |
| title_full | On functional representation
of locally m-pseudoconvex algebras |
| title_fullStr | On functional representation
of locally m-pseudoconvex algebras |
| title_full_unstemmed | On functional representation
of locally m-pseudoconvex algebras |
| title_short | On functional representation
of locally m-pseudoconvex algebras |
| title_sort | on functional representation of locally m pseudoconvex algebras |
| topic | Locally m-pseudoconvex algebras closed ideals Gelfand representation. |
| url | http://dx.doi.org/10.1155/S0161171299222235 |
| work_keys_str_mv | AT jormaarhippainen onfunctionalrepresentationoflocallympseudoconvexalgebras |