The automatic continuity for particular type of homomorphism nonassociative algebras

Abstract

Abstract Rodriguez conjecture ensures the automatic continuity of a dense range homomorphism from a complete normed nonassociative algebra into another one with zero strong radical. Rodriguez conjecture still unsolved. But there is an affirmative answer of Rodriguez conjecture presented by Rodriguez himself in [7] for particular type of nonassociative algebras called power-associative algebra. Also the authors in [11] gived an approximate solution of Rodriguez conjecture by putting a condition on multiplication algebra of a domain of such homomorphism. In this work, we give another partial solution of Rodriguez conjecture as follows: If A and B are complete normed nonassociative algebras and if  is a dense range homomorphism from A into B such that B simple with identity and multiplication algebra of B is also simple. Then  is continuous.

Keywords

• homomorphism
• nonassociative algebra
• automatic continuity