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Escaping a Neighborhood Along a Prescribed Sequence in Lie Groups and Banach Algebras
Published online by Cambridge University Press: 02 October 2019
Abstract
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It is shown that Jamison sequences, introduced in 2007 by Badea and Grivaux, arise naturally in the study of topological groups with no small subgroups, of Banach or normed algebra elements whose powers are close to identity along subsequences, and in characterizations of (self-adjoint) positive operators by the accretiveness of some of their powers. The common core of these results is a description of those sequences for which non-identity elements in Lie groups or normed algebras escape an arbitrary small neighborhood of the identity in a number of steps belonging to the given sequence. Several spectral characterizations of Jamison sequences are given, and other related results are proved.
Keywords
MSC classification
Primary:
47A10: Spectrum, resolvent
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- © Canadian Mathematical Society 2019
Footnotes
This work was supported in part by the project FRONT of the French National Research Agency (grant ANR-17-CE40-0021) and by the Labex CEMPI (ANR-11-LABX-0007-01).
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