Abdellatif Bourhim and Javad Mashreghi
Abstract: We characterize surjective maps on $B(X)$, the space of all bounded operators on an infinite-dimensional complex Banach space $X$, which satisfy $r_{T-S}(x) = 0$ if and only if $r_{\varphi(T)−\varphi(S)}(x)=0$ for every $x\in X$ and $S,T\in B(x)$. We do not assume $\varphi$ to be linear, or even additive, and thus this characterization is a step forward in generalizing some preceding results.
Journal: Integral Equations Operator Theory 76 (2013), no. 1, 95–104.
DOI: 10.1007/s00020-013-2041-9