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.
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Oudghiri, M., Souilah, K. Additive preservers of Drazin invertible operators with bounded index. Acta. Math. Sin.-English Ser. 33, 1225–1241 (2017). https://doi.org/10.1007/s10114-017-6534-3
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DOI: https://doi.org/10.1007/s10114-017-6534-3