Ascent, descent and additive preserving problems
DOI:
https://doi.org/10.24193/subbmath.2019.4.10Keywords:
Linear preserver problems, ascent, descent, semi-Fredholm operators.Abstract
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.
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