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 Ф on B（X） preserves Drazin invertible operators of index non-greater than n in both directions if and only if Ф is either...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2017-09, Vol.33 (9), p.1225-1241
Main Authors: Oudghiri, Mourad, Souilah, Khalid
Format: Article
Language:English
Subjects:
Algebra
Banach spaces
Linear operators
Mathematical analysis
Mathematics
Mathematics and Statistics
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Summary: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 Ф on B（X） preserves Drazin invertible operators of index non-greater than n in both directions if and only if Ф is either of the form Ф（T） = aATA-1 or of the form Ф（T） = aBT＊B-1 where a is a non-zero scalar, A ： X → X and B ： X＊ → X are two bounded invertible linear or conjugate linear operators.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-017-6534-3