Generalized Drazin-type spectra of Operator matrices.

Authors

  • A. Tajmouati Sidi Mohamed Ben Abdellah University.
  • M. Abkari Sidi Mohamed Ben Abdellah University.
  • M. Karmouni Cadi Ayyad University.

Keywords:

Surjective spectrum, Approximate point spectrum, Generalized Drazin spectrum, Single-valued extension property, Operator matrices

Abstract

In this paper, we investigate the limit points set of surjective and approximate point spectra of upper triangular operator matrices . We prove that σ*(MC) ∪ W=σ*(A)∪ σ*(B) where W is the union of certain holes in σ*(MC), which happen to be subsets of σlgD(B) ∩ σrgD(A), σ* ∈ {σlgD, σrgD}  are the limit points set of surjective and approximate point spectra. Furthermore, several sufficient conditions for σ* (MC) = σ* (A)∪σ* (B) holds for every C ∈ ℬ(Y,X) are given.

Author Biographies

A. Tajmouati, Sidi Mohamed Ben Abdellah University.

Faculty of Sciences Dhar Al Mahraz, Laboratory of Mathematical Analysis and Applications.

M. Abkari, Sidi Mohamed Ben Abdellah University.

Faculty of Sciences Dhar Al Mahraz, Laboratory of Mathematical Analysis and Applications.

M. Karmouni, Cadi Ayyad University.

Multi-disciplinary Faculty of Safi.

References

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Published

2018-03-15

How to Cite

[1]
A. Tajmouati, M. Abkari, and M. Karmouni, “Generalized Drazin-type spectra of Operator matrices.”, Proyecciones (Antofagasta, On line), vol. 37, no. 1, pp. 119-131, Mar. 2018.

Issue

Section

Artículos