Ascent, descent and additive preserving problems - OUDGHIRI, Mourad; SOUILAH, Khalid (Studia Universitatis Babeș-Bolyai Mathematica, 2019)
Given an integer n ≥ 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. Mathematics Subject Classification (2010): 47B49, 47L99, 47A55, 47B37.