Ascent, descent and additive preserving problems

Mourad Oudghiri, Khalid Souilah


Given an integer $n\geq 1$, we provide a complete description of all additive surjective maps, on the algebra of all bounded linear operators acting on a complex separable infinite-dimensional Hilbert space, preserving in both directions the set of all bounded linear operators with ascent (resp. descent) non-greater than $n$. In the context of Banach spaces, we consider the additive preserving problem for semi-Fredholm operators with ascent or descent non-greater than $n$.


Linear preserver problems, ascent, descent, semi-Fredholm operators

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