Journal of Operator Theory

Volume 36, Issue 2, Fall 1996 pp. 335-355.

Differentiable dependence of eigenvalues of operators in Banach spaces

Authors: Manfred Möller (1) and Anton Zettl (2)
Author institution:(1) Department of Mathematics, University of the Witwatersrand, WITS 2050, SOUTH AFRICA
(2) Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, U.S.A.

Summary: It is shown that the simple eigenvalues of operators in Banach spaces depend differentiably on the operator and the derivative is computed. This abstract result is applied to both ordinary and partial differential operators.

Keywords: Eigenvalues, parameter dependence, Fredholm operators, Sturm-Liouville problems, Schrödinger operators.

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