On an Approximate Solution to Rodriguez Conjecture
AL-Rafidain Journal of Computer Sciences and Mathematics,
2006, Volume 3, Issue 1, Pages 43-53
AbstractRickart 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.
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