On the error estimates for the Rayleigh-Schrödinger series and the Kato-Rellich perturbation series

Rekha P. Kulkarni, Balmohan V. Limaye
1989 Journal of the Australian Mathematical Society  
Let A be a simple eigenvalue of a bounded linear operator T on a Banach space X, and let (T n ) be a resolvent operator approximation of T. For large n, let S n denote the reduced resolvent associated with T n and X n , the simple eigenvalue of T n near X. It is shown that sup under the assumption that all the spectral points of T which are nearest to X belong to the discrete spectrum of T. This is used to find error estimates for the Rayleigh-Schrodinger series for X and <p with initial terms
more » ... with initial terms X n and (f n , where (p (respectively, (p n ) is an eigenvector of T (respectively, T n ) corresponding to X (respectively, X n ), and also for the Kato-Rellich perturbation series for PP n , where P (respectively, P n ) is the spectral projection for T (respectively, T n ) associated with X (respectively, X n ). 1980 Mathematics subject classification (Amer. Math. Soc.) (1985 Revision): 41 A 25, 41 A 35, 41 A 65, 47 A 70.
doi:10.1017/s1446788700030937 fatcat:jf3sgucdcjayljedhb6coyrrna