
Journal of Lie Theory 14 (2004), No. 1, 215226 Copyright Heldermann Verlag 2004 Asymptotic Products and Enlargibility of BanachLie Algebras D. Beltita Romanian Academy of Sciences, Institute of Mathematics "Simion Stoilow", P.O. Box 1764, 70700 Bucharest, Romania, dbeltita@imar.ro The paper provides a "standard" proof of a local theorem on the enlargibility of BanachLie algebras. A particularly important special case of that theorem is that a BanachLie 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 BanachLie algebras. Keywords: asymptotic product, enlargible BanachLie algebra. MSC 2000: 22E65, 17B65, 46B08. [ Fulltextpdf (176 KB)] for subscribers only. 