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On power-bounded prespectral operators

Published online by Cambridge University Press:  20 January 2009

H. R. Dowson
H. R. Dowson
Affiliation:
University of Glasgow, Glasgow G12 8QW
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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

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 20 , Issue 2 , September 1976 , pp. 173 - 175
Copyright
Copyright © Edinburgh Mathematical Society 1976

References

REFERENCES

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