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Isolated spectral points

Authors:	J J Koliha

Institution:	Department of Mathematics University of Melbourne Parkville, Victoria 3052 Australia

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 is isolated in the spectrum of a bounded linear operator if the (not necessarily closed) space $M=\{x: \lim _{n}\\|T^nx\\|^{1/n}=0\}$ is nonzero and complemented by a closed subspace satisfying $TN\subset N\subset TX$ .

Keywords:	Isolated spectral points idempotents

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