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In this chapter we investigate the stability, under small perturbations, of various spectral properties of linear operators acting between Banach spaces. The basic problems to be treated are the stability or instability of the spectrum and the perturbation of the resolvent. The results will be fundamental for the further development of perturbation theory given in the following chapters. Other subjects discussed include the stability of the Fredholm or semi-Fredholm property, of the nullity, deficiency, index, etc. The endeavor is to treat these problems for unbounded operators and for the most general perturbations.
KeywordsBanach Space Banach Algebra Closed Operator Essential Spectrum Convergent Subsequence
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