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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Mosul University
2006-07-01
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| Series: | Al-Rafidain Journal of Computer Sciences and Mathematics |
| Subjects: | |
| Online Access: | https://csmj.mosuljournals.com/article_164044_80945347d3b6b7bbf6d5be25e371c4bc.pdf |
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| Summary: | 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 /> |
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| ISSN: | 1815-4816 2311-7990 |