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1. CJM Online first
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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 Categories:46H40, 46H70 |
2. 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 Categories:46H40, 46H70 |