Local left invertibility for operator tuples and noncommutative localizations

摘要

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 Fréchet space. We prove that the canonical homomorphism U(g)→Og of the universal enveloping algebra U(g) of a nilpotent Lie algebra g into its Arens-Michael envelope Og is the Taylor localization whenever g has normal growth.