Local Spectral Radius Preservers

摘要

We characterize surjective maps on ({fancyscript{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 ({{{rm r}_{varphi(T)-varphi(S)}(x) = 0}}) for every ({x in X}) and ({{S, T in fancyscript{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.