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Automatic Continuity of Homomorphisms in Non-associative Banach Algebras
  • C-H. Chu,
    School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS, UK
  • M. V. Velasco,
    Dpto. de Analisis Matematico, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
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Abstract

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 automatic continuity, non-associative algebra, spectrum, rare operator, rare element
MSC Classifications: 46H40, 46H70 show english descriptions Automatic continuity
Nonassociative topological algebras [See also 46K70, 46L70] 46H40 - Automatic continuity
46H70 - Nonassociative topological algebras [See also 46K70, 46L70]
 
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