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Local left invertibility for operator tuples and noncommutative localizations

2009-01-01
Dosiev, Anar
In the paper we propose an operator approach to the noncommutative Taylor localization problem based on the local left invertibility for operator tuples acting on a Frechet space. We prove that the canonical homomorphism U(g) -> O(g) of the universal enveloping algebra U(g) of a nilpotent Lie algebra g into its Arens-Michael envelope O(g) is the Taylor localization whenever g has normal growth.