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Journal of Operator Theory

Volume 46, Issue 3, Supplementary 2001  pp. 593-603.

Spectral conditions for the nilpotency of Lie algebras

Authors:  Daniel Beltita
Author institution: Institute of Mathematics of the Romanian Academy, P.O. Box 1--764, 70700 Bucharest, Romania

Summary:  In the paper it is proved that each of the following conditions below is suffici ent for the nilpotency of a solvable Lie algebra. TheyareformulatedbymeansofthespectrumofaBanachspacerepresentationofaLiealgebra,introducedbyC.Ottin[9]. 1) The validity of the projection property of the spectrum on Lie subalgebras imposedtoonlyonerepresentation. 2) The existence of representations with spectra of arbitrarily small diameters withrespecttoafixednormonthegivenLiealgebra.

Keywords:  Lie algebra homology, Taylor joint spectrum, projection property, spectral diameter


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