作者：Ting; ZHANG; Jin; Chuan; HOUbanachspacesnilpotentoperatorsperturbationsadditivepreservers
摘要：Let X be a Banach space over F(= R or C) with dimension greater than 2. Let N(X) be the set of all nilpotent operators and B0(X) the set spanned by N(X). We give a structure result to the additive maps on FI + B0(X) that preserve rank-1 perturbation of scalars in both directions. Based on it, a characterization of surjective additive maps on FI + B0(X) that preserve nilpotent perturbation of scalars in both directions are obtained. Such a map Φ has the form either Φ(T) = cAT A-1+ φ(T)I for all T ∈ FI + B0(X) or Φ(T) = cAT*A-1+ φ(T)I for all T ∈ FI + B0(X), where c is a nonzero scalar,A is a τ-linear bijective transformation for some automorphism τ of F and φ is an additive functional.In addition, if dim X = ∞, then A is in fact a linear or conjugate linear invertible bounded operator.
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