1. CJM Online first
|Automatic Continuity of Homomorphisms in Non-associative Banach Algebras|
We introduce the concept of a rare element in a non-associative normed algebra and show that the existence of such element is the only obstruction to continuity of a surjective homomorphism from a non-associative Banach algebra to a unital normed algebra with simple completion. Unital associative algebras do not admit any rare element and hence automatic continuity holds.
Keywords:automatic continuity, non-associative algebra, spectrum, rare operator, rare element