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Journal of Lie Theory 19 (2009), No. 2, 223--230
Copyright Heldermann Verlag 2009

Local Spectral Radius Formulas on Compact Lie Groups

Nils Byrial Andersen
Alssundgymnasiet Sönderborg, Grundtvigs Allé 86, 6400 Sönderborg, Denmark

Marcel de Jeu
Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands

We determine the local spectrum of a central element of the complexified universal enveloping algebra of a compact connected Lie group at a smooth function as an element of Lp(G). Based on this result we establish a corresponding local spectral radius formula.

Keywords: Compact Lie group, universal enveloping algebra, local spectrum, local spectral radius, local spectral radius formula.

MSC: 22E30; 47A11

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