Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Isolated spectral points

Author(s): 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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