On spectral properties of perturbed operators

Nair, M. Thamban

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

On spectral properties of perturbed operators
HTML articles powered by AMS MathViewer

by M. Thamban Nair PDF

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

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.

References

F. O. Farid and P. Lancaster, Spectral properties of diagonally dominant infinite matrices. I, Proc. Roy. Soc. Edinburgh Sect. A 111 (1989), no. 3-4, 301–314. MR 1007527, DOI 10.1017/S0308210500018576
F. O. Farid and P. Lancaster, Spectral properties of diagonally dominant infinite matrices. II, Linear Algebra Appl. 143 (1991), 7–17. MR 1077721, DOI 10.1016/0024-3795(91)90003-F
F. O. Farid, Spectral properties of perturbed linear operators and their application to infinite matrices, Proc. Amer. Math. Soc. 112 (1991), no. 4, 1013–1022. MR 1057943, DOI 10.1090/S0002-9939-1991-1057943-2

Approximation and localization of eigenelements

M. Thamban Nair, Approximation of spectral sets and spectral subspaces in Banach spaces, J. Indian Math. Soc. (N.S.) 54 (1989), no. 1-4, 187–200. MR 1069270
M. Thamban Nair, On iterative refinements for spectral sets and spectral subspaces, Numer. Funct. Anal. Optim. 10 (1989), no. 9-10, 1019–1037. MR 1035655, DOI 10.1080/01630568908816343
Paul Rosenbloom, Perturbation of linear operators in Banach spaces, Arch. Math. (Basel) 6 (1955), 89–101. MR 68118, DOI 10.1007/BF01900211
Angus Ellis Taylor and David C. Lay, Introduction to functional analysis, 2nd ed., John Wiley & Sons, New York-Chichester-Brisbane, 1980. MR 564653
G. W. Stewart, Error bounds for approximate invariant subspaces of closed linear operators, SIAM J. Numer. Anal. 8 (1971), 796–808. MR 293831, DOI 10.1137/0708073