Journal of Lie Theory 14 (2004), No. 1, 215--226
Copyright Heldermann Verlag 2004
Asymptotic Products and Enlargibility of Banach-Lie Algebras
Romanian Academy of Sciences, Institute of Mathematics "Simion Stoilow", P.O. Box 1-764, 70700 Bucharest, Romania, email@example.com
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.
Keywords: asymptotic product, enlargible Banach-Lie algebra.
MSC 2000: 22E65, 17B65, 46B08.
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