Abstract
Given two different complex numbers a and b, a bounded linear operator T acting on an infinite-dimensional complex Hilbert space H is said to be {a, b}-quadratic if (T − a)(T − b) = 0. We provide in this paper a complete description of all surjective maps Φ (not necessarily additive) on the algebra \({\cal B}(H)\) of all bounded linear operators on H that satisfy S − λT is {a, b}-quadratic if and only if Φ(S) − λΦ(T) is {a, b}-quadratic for every \(S,T \in {\cal B}(H)\) and λ ∈ ℂ.
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Oudghiri, M., Souilah, K. Nonlinear preservers involving quadratic operators. Anal Math 47, 867–879 (2021). https://doi.org/10.1007/s10476-021-0103-9
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DOI: https://doi.org/10.1007/s10476-021-0103-9