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Invertible Operators on Certain Banach Spaces

Published online by Cambridge University Press:  20 November 2018

J.-M. Belley
J.-M. Belley*
Affiliation:
Faculté des Sciences, Université de Sherbrooke, Sherbrooke que., CanadaJ1K 2R1
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It has long been the practice in the theory of Hilbert spaces to use the Fourier series expansion (i.e. the Levy inversion formula) for the resolution of the identity associated with a unitary operator to obtain results for this operator, and hence for any power bounded invertible operator on such spaces since they are necessarily isomorphic to unitary operators [5, p. 1945]. Though many important power bounded operators on Banach spaces are not spectral [6, p. 1045-1051] the approach of this paper permits us to deduce for such operators results similar to those known for spectral operators.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 2 , 01 June 1977 , pp. 153 - 160
Copyright
Copyright © Canadian Mathematical Society 1977

References

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