Isolated spectral points
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- by J. J. Koliha PDF
- Proc. Amer. Math. Soc. 124 (1996), 3417-3424 Request permission
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 $TN\subset N\subset TX$.References
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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
- Received by editor(s): February 28, 1995
- Received by editor(s) in revised form: May 9, 1995
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 3417-3424
- MSC (1991): Primary 46H30, 47A10, 47A60
- DOI: https://doi.org/10.1090/S0002-9939-96-03449-1
- MathSciNet review: 1342031