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On power-bounded prespectral operators
Published online by Cambridge University Press: 20 January 2009
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Foguel (8) and Fixman (7) independently proved that an invertible spectral operator, which is power-bounded, is of scalar type. Their proofs rely heavily on a result of Dunford on spectral operators whose resolvents satisfy a growth condition. (See Lemma 3.16 of (6, p. 609).) Observe that the resolvent of an invertible power-bounded operator T satisfies an inequality of the form
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- Research Article
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- Proceedings of the Edinburgh Mathematical Society , Volume 20 , Issue 2 , September 1976 , pp. 173 - 175
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- Copyright © Edinburgh Mathematical Society 1976