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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Isolated spectral points


Author: J. J. Koliha
Journal: Proc. Amer. Math. Soc. 124 (1996), 3417-3424
MSC (1991): Primary 46H30, 47A10, 47A60
MathSciNet review: 1342031
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Abstract: The paper studies isolated spectral points of elements of Banach algebras and of bounded linear operators in terms of the existence of idempotents, and gives an elementary characterization of spectral idempotents. It is shown that $0$ is isolated in the spectrum of a bounded linear operator $T$ if the (not necessarily closed) space $M=\{x: \lim _{n}\|T^nx\|^{1/n}=0\}$ is nonzero and complemented by a closed subspace $N$ satisfying $TN\subset N\subset TX$.


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Additional Information

J. J. Koliha
Affiliation: Department of Mathematics\ University of Melbourne\ Parkville, Victoria 3052\ Australia
Email: jjk@mundoe.maths.mu.oz.au

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03449-1
PII: S 0002-9939(96)03449-1
Keywords: Isolated spectral points, idempotents
Received by editor(s): February 28, 1995
Received by editor(s) in revised form: May 9, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society