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Search: MSC category 46H70 ( Nonassociative topological algebras [See also 46K70, 46L70] )

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1. CJM 2012 (vol 65 pp. 989)

Chu, C-H.; Velasco, M. V.
 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 elementCategories:46H40, 46H70