Banach Journal of Mathematical Analysis

Additive maps preserving Drazin invertible operators of index n

Mostafa Mbekhta, Mourad Oudghiri, and Khalid Souilah

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Abstract

Given an integer n2, in this article we provide a complete description of all additive surjective maps on the algebra of all bounded linear operators acting on an infinite-dimensional complex Banach space, preserving in both directions the set of Drazin invertible operators of index n.

Article information

Source
Banach J. Math. Anal., Volume 11, Number 2 (2017), 416-437.

Dates
Received: 4 February 2016
Accepted: 1 July 2016
First available in Project Euclid: 18 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1489802494

Digital Object Identifier
doi:10.1215/17358787-0000011X

Mathematical Reviews number (MathSciNet)
MR3625792

Zentralblatt MATH identifier
06754296

Subjects
Primary: 47B49: Transformers, preservers (operators on spaces of operators)
Secondary: 47L99: None of the above, but in this section 47A55: Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15] 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)

Keywords
linear preserver problems Drazin inverse ascent descent

Citation

Mbekhta, Mostafa; Oudghiri, Mourad; Souilah, Khalid. Additive maps preserving Drazin invertible operators of index $n$. Banach J. Math. Anal. 11 (2017), no. 2, 416--437. doi:10.1215/17358787-0000011X. https://projecteuclid.org/euclid.bjma/1489802494


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