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Continuous homomorphisms of Arens-Michael algebras. (English) Zbl 1028.46064

Summary: It is shown that every continuous homomorphism of Arens-Michael algebras can be obtained as the limit of a morphism of certain projective systems consisting of Fréchet algebras. Based on this, we prove that a complemented subalgebra of an uncountable product of Fréchet algebras is topologically isomorphic to the product of Fréchet algebras.

MSC:

46H05 General theory of topological algebras
46M10 Projective and injective objects in functional analysis
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