Journal of Lie Theory EMIS ELibM Electronic Journals Journal of Lie Theory
Vol. 14, No. 1, pp. 215--226 (2004)

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Asymptotic Products and Enlargibility of Banach-Lie Algebras

Daniel Beltita

Daniel Beltita
Institute of Mathematics ``Simion Stoilow'' of the Romanian Academy
P.O. Box 1-764
RO-70700 Bucharest

Abstract: The paper provides a ``standard'' proof of a local theorem on 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 enlargibility of asymptotic products of contractive Banach-Lie algebras.

Keywords: asymptotic product; enlargible Banach-Lie algebra

Classification (MSC2000): 22E65; 17B65, 46B08

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Electronic version published on: 29 Jan 2004. This page was last modified: 1 Sep 2004.

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