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Automatic Continuity of Homomorphisms in Non-associative Banach Algebras
Published online by Cambridge University Press: 20 November 2018
Abstract
We introduce the concept of a rare element in a non-associative normed algebra and show that the existence of such an 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 elements, and hence automatic continuity holds.
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- Copyright © Canadian Mathematical Society 2013