Vol. 68, No. 1, 1977

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A perturbation theorem for spectral operators

Dieter Lutz

Vol. 68 (1977), No. 1, 127–134

This note is concerned with analytic perturbations of spectral operators. It is shown that under small perturbations simple isolated eigenvalues remain simple and isolated and depend holomorphically upon the perturbation parameter. As one would expect the bounds are rather complicated in the case of a spectral operator with general quasinilpotent part. For scalar operators, however, these bounds become simple and reproduce in the selfadjoint case those given by F. W. Schäfke.

Mathematical Subject Classification 2000
Primary: 47B40
Secondary: 47A55
Received: 5 May 1976
Published: 1 January 1977
Dieter Lutz