Geodesic
Automatic Continuity of Homomorphisms in Non-associative Banach Algebras
Canadian journal of mathematics, Tome 65 (2013) no. 5, pp. 989-1004

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DOI

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.
DOI : 10.4153/CJM-2012-049-6
Mots-clés : 46H40, 46H70, automatic continuity, non-associative algebra, spectrum, rare operator, rare element 
Chu, C-H.; Velasco, M. V. Automatic Continuity of Homomorphisms in Non-associative Banach Algebras. Canadian journal of mathematics, Tome 65 (2013) no. 5, pp. 989-1004. doi: 10.4153/CJM-2012-049-6
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     author = {Chu, C-H. and Velasco, M. V.},
     title = {Automatic {Continuity} of {Homomorphisms} in {Non-associative} {Banach} {Algebras}},
     journal = {Canadian journal of mathematics},
     pages = {989--1004},
     year = {2013},
     volume = {65},
     number = {5},
     doi = {10.4153/CJM-2012-049-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2012-049-6/}
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