On an Approximate Solution to Rodriguez Conjecture
Rickart Theorem ensures the automatic continuity of a dense range homomorphism from a Banach algebra into a strongly Semisimple Banach algebra. Rodriguez conjecture is an extension of Rickart theorem in order to include the nonassociative algebras as follows:<br /> <span style="text-de...
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Mosul University
2006-07-01
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| Series: | Al-Rafidain Journal of Computer Sciences and Mathematics |
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| Online Access: | https://csmj.mosuljournals.com/article_164044_80945347d3b6b7bbf6d5be25e371c4bc.pdf |
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| author | Amir Mohammed Ruqiya Balu |
| author_facet | Amir Mohammed Ruqiya Balu |
| author_sort | Amir Mohammed |
| collection | DOAJ |
| description | Rickart Theorem ensures the automatic continuity of a dense range homomorphism from a Banach algebra into a strongly Semisimple Banach algebra. Rodriguez conjecture is an extension of Rickart theorem in order to include the nonassociative algebras as follows:<br /> <span style="text-decoration: underline;">Rodriguez conjecture</span>:Every densely valued homomorphism from a complete normed nonassociative algebra into another one with zero strong radical is continuous.<br /> There is an affirmative answer of Rodriguez conjecture in particular case of power-associative algebra’s. In this work, we give an approximate solution of Rodriguez conjecture:<br /> If A and B are complete normed nonassociative algebras and if f is a dense range homomorphism from A into B such that M(A) (the multiplication algebra of A) is full and B is strongly Semisimple, then f is continuous.<br /> Finally, we give a Gelfand theorem on automatic continuity as a corollary and as an applied example of our approximate solution of Rodriguez conjecture.<br /> |
| format | Article |
| id | doaj-art-89953dfec6b54857a8daa9cf7e1e3b83 |
| institution | OA Journals |
| issn | 1815-4816 2311-7990 |
| language | English |
| publishDate | 2006-07-01 |
| publisher | Mosul University |
| record_format | Article |
| series | Al-Rafidain Journal of Computer Sciences and Mathematics |
| spelling | doaj-art-89953dfec6b54857a8daa9cf7e1e3b832025-08-20T02:09:37ZengMosul UniversityAl-Rafidain Journal of Computer Sciences and Mathematics1815-48162311-79902006-07-0131435310.33899/csmj.2006.164044164044On an Approximate Solution to Rodriguez ConjectureAmir Mohammed0Ruqiya Balu1Department of Mathematics College of Education University of Mosul, Mosul, IraqCollege of Education, University of Mosul, IraqRickart Theorem ensures the automatic continuity of a dense range homomorphism from a Banach algebra into a strongly Semisimple Banach algebra. Rodriguez conjecture is an extension of Rickart theorem in order to include the nonassociative algebras as follows:<br /> <span style="text-decoration: underline;">Rodriguez conjecture</span>:Every densely valued homomorphism from a complete normed nonassociative algebra into another one with zero strong radical is continuous.<br /> There is an affirmative answer of Rodriguez conjecture in particular case of power-associative algebra’s. In this work, we give an approximate solution of Rodriguez conjecture:<br /> If A and B are complete normed nonassociative algebras and if f is a dense range homomorphism from A into B such that M(A) (the multiplication algebra of A) is full and B is strongly Semisimple, then f is continuous.<br /> Finally, we give a Gelfand theorem on automatic continuity as a corollary and as an applied example of our approximate solution of Rodriguez conjecture.<br />https://csmj.mosuljournals.com/article_164044_80945347d3b6b7bbf6d5be25e371c4bc.pdfautomatic continuityrickart theorembanach algebrarodriguez conjecturegelfand theorem |
| spellingShingle | Amir Mohammed Ruqiya Balu On an Approximate Solution to Rodriguez Conjecture Al-Rafidain Journal of Computer Sciences and Mathematics automatic continuity rickart theorem banach algebra rodriguez conjecture gelfand theorem |
| title | On an Approximate Solution to Rodriguez Conjecture |
| title_full | On an Approximate Solution to Rodriguez Conjecture |
| title_fullStr | On an Approximate Solution to Rodriguez Conjecture |
| title_full_unstemmed | On an Approximate Solution to Rodriguez Conjecture |
| title_short | On an Approximate Solution to Rodriguez Conjecture |
| title_sort | on an approximate solution to rodriguez conjecture |
| topic | automatic continuity rickart theorem banach algebra rodriguez conjecture gelfand theorem |
| url | https://csmj.mosuljournals.com/article_164044_80945347d3b6b7bbf6d5be25e371c4bc.pdf |
| work_keys_str_mv | AT amirmohammed onanapproximatesolutiontorodriguezconjecture AT ruqiyabalu onanapproximatesolutiontorodriguezconjecture |