Annals of Functional Analysis

The perturbation class of algebraic operators and applications

Mourad Oudghiri and Khalid Souilah

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In this article, we completely describe the perturbation class, the commuting perturbation class, and the topological interior of the class of all bounded linear algebraic operators. As applications, we also focus on the stability of the essential ascent spectrum and the essential descent spectrum under finite-rank perturbations.

Article information

Ann. Funct. Anal., Volume 9, Number 3 (2018), 426-434.

Received: 29 June 2017
Accepted: 15 September 2017
First available in Project Euclid: 6 February 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A55: Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15]
Secondary: 47A10: Spectrum, resolvent 47A99: None of the above, but in this section

perturbation classes problem algebraic operators


Oudghiri, Mourad; Souilah, Khalid. The perturbation class of algebraic operators and applications. Ann. Funct. Anal. 9 (2018), no. 3, 426--434. doi:10.1215/20088752-2017-0057.

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