Completeness Criteria of the Space of Generalized Eigenvectors of Non-Self-Adjoint Operators

Aref Jeribi ()
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Aref Jeribi: University of Sfax, Department of Mathematics

Chapter Chapter 6 in Perturbation Theory for Linear Operators, 2021, pp 177-205 from Springer

Abstract: Abstract In this chapter, we recall some Keldysh results that are not only specific for Hilbert spaces, but they have been formulated for operators in Banach spaces. We also discuss some theorems on denseness of the generalized eigenvectors of a compact operator or an operator with compact resolvent and different conditions assuring the completeness of the system of root subspaces. In the selection of the material, we present as fully as the various existing results.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-16-2528-2_6

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DOI: 10.1007/978-981-16-2528-2_6

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