On spectral properties of perturbed operators

Nair, M. Thamban

doi:10.1090/S0002-9939-1995-1242098-5

On spectral properties of perturbed operators
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by M. Thamban Nair

Proc. Amer. Math. Soc. 123 (1995), 1845-1850

DOI: https://doi.org/10.1090/S0002-9939-1995-1242098-5

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Abstract:

Farid (1991) has given an estimate for the norm of a perturbation V required to obtain an eigenvector for the perturbed operator $T + V$ within a given ball centered at a given eigenvector of the unperturbed (closed linear) operator T. A similar result is derived from a more general result of the author (1989) which also guarantees that the corresponding eigenvalue is simple and also that the eigenpair is the limit of a sequence obtained in an iterative manner.

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