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Continuity Properties of Operator Spectra

Published online by Cambridge University Press:  20 November 2018

Nicholas J. Bezak
Affiliation:
Clarion State College, Clarion, Pennsylvania
Martin Eisen
Affiliation:
Temple University, Philadelphia, Pennsylvania
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Abstract

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This paper is devoted to the study of convergence and variation of operator spectra with respect to the distance G of Gokhburg and Markus [5] for subspaces and linear operators in a Banach space. We use the convention of Kato [7] and refer to convergence with respect to G as generalizedconvergence.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Berkson, E., Some metrics on the subspaces of a Banach space, Pacific Journal of Math. 13 (1963), 721.Google Scholar
2. Bezak, N. J., Topological and spectral properties of the set of linear operators in a Banach space, Ph.D. Thesis, University of Pittsburgh, 1967.Google Scholar
3. Dunford, N. and Schwartz, J. T., Linear operators, Vol. 1 (Interscience, New York, 1958). 4. H. A. Gindler and Taylor, A. E., The minimum modulus of a linear operator and its use in spectral theory, Studia Mathematica 22 (1962), 1541.Google Scholar
4. Gokhburg, I. C. and Markus, A. S., Two theorems on the opening between subspaces of a Banach space, Uspekhi Mat. Nauk. 89 (1959), 135140 (in Russian).Google Scholar
5. Hausdorff, F., Mengenlehre (Dover, New York, 1944).Google Scholar
6. Kato, T., Perturbation theory for linear operators (Springer-Verlag, New York, 1966).Google Scholar
7. Krein, M. G., M. A. Krasnoselski and Milman, D. P., Concerning the deficiency numbers of linear operators in Banach spaces and some geometric questions, Sbornik Trudov Inst. A. N. Ukr. S. S. R. 11 (1948) (in Russian).Google Scholar
8. Michael, E., Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 151182.Google Scholar
10. Newburgh, J. D., A topology for closed operators, Ann. of Math. 53 (1951), 250255.Google Scholar
11. Newburgh, J. D. The variation of spectra, Duke Math. Journal 18 (1951), 165176.Google Scholar
12. Gokhburg, I. C. and Krein, M. G., The basic propositions on defect numbers, root numbers, and indices of linear operators, Uspekhi Mat. Nauk. 12 (1957) 2 (74), 43-118 [Amer. Math. Soc. Trans.-Ser. 2, 18 (1960), 185264].Google Scholar
13. Rota, G. C., Extension theory of differential operators I, Comm. Pure and App. Math. 11 (1958), 2365.Google Scholar
14. Taylor, A. E., Spectral theory of closed distributative operators, Acta Math. 84 (1951), 189224.Google Scholar
15. Taylor, A. E. Introduction to functional analysis (Wiley, New York, 1958).Google Scholar