The Fredholm radius of a bundle of closed linear operators
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- by E.-O. Liebetrau PDF
- Proc. Amer. Math. Soc. 70 (1978), 67-71 Request permission
Abstract:
Given a bundle of linear operators $T - \lambda S$, where T is closed and S is bounded, a sequence $\{ {\delta _m}(T:S)\}$ of extended real numbers is defined. If T is a Fredholm operator, the limit ${\lim \delta _m}{(T:S)^{1/m}}$ exists and is equal to the supremum of all $r > 0$ such that $T - \lambda S$ is a Fredholm operator for $|\lambda | < r$.References
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H. Bart and D. C. Lay, The stability radius of a bundle of closed linear operators, Univ. of Maryland, TR-76-11 (1976), 1-23.
- K.-H. Förster and M. A. Kaashoek, The asymptotic behaviour of the reduced minimum modulus of a Fredholm operator, Proc. Amer. Math. Soc. 49 (1975), 123–131. MR 372660, DOI 10.1090/S0002-9939-1975-0372660-0
- Tosio Kato, Perturbation theory for nullity, deficiency and other quantities of linear operators, J. Analyse Math. 6 (1958), 261–322. MR 107819, DOI 10.1007/BF02790238
- Arnold Lebow and Martin Schechter, Semigroups of operators and measures of noncompactness, J. Functional Analysis 7 (1971), 1–26. MR 0273422, DOI 10.1016/0022-1236(71)90041-3 E.-O. Liebetrau, Über die Fredholmmenge linearer Operatoren, Dissertation, Dortmund, 1972.
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 70 (1978), 67-71
- MSC: Primary 47B30
- DOI: https://doi.org/10.1090/S0002-9939-1978-0477858-1
- MathSciNet review: 0477858