Abstract
Let X be a complex Banach space with and be a standard operator algebra on X. Let k be a positive integer. For , the k-commutator of A and B is defined by with . Let be a map. We say that is strong k-commutativity preserving if for any . In this paper, it is shown that, if the range of contains all operators of rank one, then is strong k-commutativity preserving if and only if there exist a functional and a scalar with such that for all .
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