On left and right poles of the resolvent. (English) Zbl 1210.47010
Summary: In this article, we study left and right poles of the resolvent of a bounded operator defined on an infinite-dimensional complex Banach space. In particular, some spectral decompositions associated with left and right poles of the resolvent are established, and the components of the upper and lower semi B-Fredholm regions are studied by means of the localized single-valued extension property.
MSC:
47A10 | Spectrum, resolvent |
47A11 | Local spectral properties of linear operators |
47A53 | (Semi-) Fredholm operators; index theories |
47A55 | Perturbation theory of linear operators |