Advertisement

Problem of descent spectrum equality

  • Abdelaziz TajmouatiEmail author
  • Hamid Boua
Article
  • 22 Downloads

Abstract

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 \(\sigma _{desc}(T)=\sigma _{desc}(T, {\mathcal {B}}(X))\)?

Keywords

Descend Pole Resolvent Spectrum 

Mathematics Subject Classification

47A10 47A11 

Notes

Acknowledgements

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

References

  1. 1.
    Aiena, P.: Fredholm and Local Spectral Theory with Applications to Multipliers. Kluwer Academic Press, Dordrecht (2004)zbMATHGoogle Scholar
  2. 2.
    Haïly, A., Kaidi, A., Rodríguez Palacios, A.: Algebra descent spectrum of operators. Isr. J. Math. 177, 349–368 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Laursen, K.B., Neumann, M.M.: Introduction to Local Spectral Theory. Clarendon Press, Oxford (2000)zbMATHGoogle Scholar
  4. 4.
    Lay, D.C.: Spectral analysis using ascent, descent, nullity and defect. Math. Ann. 184, 197–214 (1970)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Miller, T.L., Miller, V.G., Smith, R.C.: Bishop’s property (\(\beta \)) and the Césaro operator. J. Lond. Math. Soc. (2) 58, 197–207 (1998)CrossRefzbMATHGoogle Scholar
  6. 6.
    Müller, V.: Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras. Operator Theory Advances and Applications, vol. 139, 2nd edn. Birkhäuser, Basel (2007)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2018

Authors and Affiliations

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

Personalised recommendations