Asymptotic Products and Enlargibility of Banach-Lie Algebras

摘要

The paper provides a "standard" proof of a local theorem on the enlargibility of Banach-Lie algebras. A particularly important special case of that theorem is that a Banach-Lie algebra is enlargible provided it has a dense locally finite subalgebra. The theorem is due to V. Pestov, who proved it by techniques of nonstandard analysis. The present proof uses a theorem concerning the enlargibility of asymptotic products of contractive Banach-Lie algebras.