Spectral perturbation theory for bounded linear operators

Code: MA732 | L-T-P-C: 4-0-0-8

MA732 Spectral perturbation theory for bounded linear operators L-T-P-C [4-0-0-8]

Prerequisites: Nil

Banach space valued analytic functions, bounded linear operators in Banach spaces, adjoint operators, projection operators. Resolvent and spectra of bounded linear operators, isolated spectral values, spectral projections and spectral decompositions, spectra of adjoint operators. Linear and analytic perturbation theory for discrete spectra, continuity and analyticity of the resolvent operators, perturbation of the spectral projections, perturbation series for spectral projections and eigenvalues, a theorem of Motzkin-Taussky.

Texts/References:

1. B. V. Limaye, Spectral Perturbation and Approximation with Numerical Experiments, Proceedings of CMA, Australian National University, Vol.13, 1986.
2. T. Kato, Perturbation Theory for Linear operators, Springer, 1980.
3. G.W. Stewart and J. G. Sun, Matrix Perturbation Theory, Academic Press, 1990.