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Perturbations of spectra of operator matrices. (English) Zbl 1019.47003
Let M C denote the operator matrix M C =AC0B, acting on the direct sum of Banach or orthogonal direct sum of Hilbert spaces. Charecterizations of the intersection of the left or right spectra, the left or right Fredholms spectra, and the Weyl or Browder spectra of all operators M C when C runs in (C,Y) are considered. Applications to perturbations of the left and right spectra are also obtained.
MSC:
47A10Spectrum and resolvent of linear operators
47A53(Semi-)Fredholm operators; index theories
47A55Perturbation theory of linear operators