Automatic Continuity of Homomorphisms in Non-associative Banach Algebras

Chu, C-H. ; Velasco, M. V.

Canadian journal of mathematics, Tome 65 (2013) no. 5, pp. 989-1004

Résumé

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.

Détail

DOI : 10.4153/CJM-2012-049-6

Mots-clés : 46H40, 46H70, automatic continuity, non-associative algebra, spectrum, rare operator, rare element

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