On a Schauder and Riesz Bases of Eigenvectors of an Analytic Operator

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

Chapter Chapter 10 in Perturbation Theory for Linear Operators, 2021, pp 335-359 from Springer

Abstract: Abstract This chapter deals with Schauder and Riesz bases of eigenvectors of a family of non-normal operators. Indeed, we generalize some results due to Nagy in [29] and we extend the main result in [7] to Schauder basis in a separable Banach space. Second, we investigate under sufficient conditions assuring the existence of a Riesz basis in a Hilbert space X, formed by eigenvectors of the perturbed operator $$T(\varepsilon )$$ T ( ε ) . We also study the existence of a finitely spectral Riesz basis of a family of non-normal operators including the spectral Riesz basis of subspaces and the Riesz basis of subspaces.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-16-2528-2_10

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DOI: 10.1007/978-981-16-2528-2_10

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