# Additive preservers of Drazin invertible operators with bounded index

Additive preservers of Drazin invertible operators with bounded index Let B(X) be the algebra of all bounded linear operators on an infinite-dimensional complex or real Banach space X. Given an integer n ≥ 1, we show that an additive surjective map Φ on B(X) preserves Drazin invertible operators of index non-greater than n in both directions if and only if Φ is either of the form Φ(T) = αATA −1 or of the form Φ(T) = αBT *B −1 where α is a non-zero scalar, A: X → X and B: X* → X are two bounded invertible linear or conjugate linear operators. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematica Sinica, English Series Springer Journals

# Additive preservers of Drazin invertible operators with bounded index

, Volume 33 (9) – Jun 28, 2017
17 pages

Publisher
Springer Journals
Copyright © 2017 by Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany
Subject
Mathematics; Mathematics, general
ISSN
1439-8516
eISSN
1439-7617
D.O.I.
10.1007/s10114-017-6534-3
Publisher site
See Article on Publisher Site

### Abstract

Let B(X) be the algebra of all bounded linear operators on an infinite-dimensional complex or real Banach space X. Given an integer n ≥ 1, we show that an additive surjective map Φ on B(X) preserves Drazin invertible operators of index non-greater than n in both directions if and only if Φ is either of the form Φ(T) = αATA −1 or of the form Φ(T) = αBT *B −1 where α is a non-zero scalar, A: X → X and B: X* → X are two bounded invertible linear or conjugate linear operators.

### Journal

Acta Mathematica Sinica, English SeriesSpringer Journals

Published: Jun 28, 2017

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