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Automatic Continuity of Homomorphisms in Non-associative Banach Algebras

Published online by Cambridge University Press:  20 November 2018

C-H. Chu  and
M. V. Velasco
C-H. Chu
Affiliation:
School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS, UK, e-mail: c.chu@qmul.ac.uk
M. V. Velasco
Affiliation:
Dpto. de Analisis Matematico, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain, e-mail: vvelasco@ugr.esc.chu@qmul.ac.uk
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Abstract

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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.

Keywords

46H4046H70automatic continuitynon-associative algebraspectrumrare operatorrare element
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 65 , Issue 5 , 01 October 2013 , pp. 989 - 1004
Copyright
Copyright © Canadian Mathematical Society 2013

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