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On Meromorphic Operators, I

Published online by Cambridge University Press:  20 November 2018

S. R. Caradus
S. R. Caradus*
Affiliation:
Queen's University, Kingston, Ontario
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If X is a complex Banach space and B(X) denotes the space of bounded linear operators on X, then the class of meromorphic operators consists of those T in B(X) such that the non-zero points of σ(T) are poles of the resolvent Rλ(T). If we also require that each non-zero eigenvalue of T have finite multiplicity, members of the class ⊆ so defined have been called operators of Riesz type. and have been studied in (2, 6, 7) and (1,4) respectively.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 723 - 736
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Caradus, S. R., Operators of Riesz type, Pacific J. Math., 18 (1966), 61–71.Google Scholar
2. Derr, J. and Taylor, A. E., Operators of meromorphic type with multiple poles of the resolvent, Pacific J. Math., 12 (1962), 85–111.Google Scholar
3. Loomis, L. H., An introduction to abstract harmonic analysis (Princeton, 1953).Google Scholar
4. Ruston, A. F., Operators with Fredholm theory, J. London Math. Soc., 29 (1954), 318–326.Google Scholar
5. Taylor, A. E., Introduction to functional analysis (New York, 1958).Google Scholar
6. Taylor, A. E., Mittag Leffler expansions and spectral theory, Pacific J. Math., 10, 3 (1960), 1049–1066.Google Scholar
7. Taylor, A. E., Spectral theory and Mittag Leffler type expansions of the resolvent, Proc. Int. Symp. Linear Spaces, Jerusalem, 1960, pp. 426–440.Google Scholar