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On an Approximate Solution to Rodriguez Conjecture | ||
| AL-Rafidain Journal of Computer Sciences and Mathematics | ||
| Article 13, Volume 3, Issue 1, 2006, Pages 43-53 PDF (376.77 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.33899/csmj.2006.164044 | ||
| Authors | ||
| Amir A. Mohammed1; Ruqiya N. Balu2 | ||
| 1Department of Mathematics College of Education University of Mosul, Mosul, Iraq | ||
| 2College of Education, University of Mosul, Iraq | ||
| Abstract | ||
| 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: Rodriguez conjecture:Every densely valued homomorphism from a complete normed nonassociative algebra into another one with zero strong radical is continuous. 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: 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. Finally, we give a Gelfand theorem on automatic continuity as a corollary and as an applied example of our approximate solution of Rodriguez conjecture. | ||
| Keywords | ||
| automatic continuity; Rickart Theorem; Banach algebra; Rodriguez conjecture; Gelfand theorem | ||
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