Problem of descent spectrum equality

  • Abdelaziz TajmouatiEmail author
  • Hamid Boua


Let \({\mathcal {B}}(X)\) be the algebra of all bounded operators acting on an infinite dimensional complex Banach space X. We say that an operator \(T \in {\mathcal {B}}(X)\) satisfies the problem of descent spectrum equality, if the descent spectrum of T as an operator coincides with the descent spectrum of T as an element of the algebra of all bounded linear operators on X. In this paper we are interested in the problem of descent spectrum equality. Specifically, the problem is to consider the following question: let \(T \in {\mathcal {B}}(X)\) such that \(\sigma (T)\) has non empty interior, under which condition on T does \(\sigma _{desc}(T)=\sigma _{desc}(T, {\mathcal {B}}(X))\)?


Descend Pole Resolvent Spectrum 

Mathematics Subject Classification

47A10 47A11 



We wish to thank the referee for his valuable comments and suggestions.


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Copyright information

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Authors and Affiliations

  1. 1.Laboratory of Mathematical Analysis and Applications, Faculty of Sciences Dhar El MahrazSidi Mohamed Ben Abdellah UniversityFezMorocco

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