Characterizations of α-centralizable mappings on B(X)
Let X be a Banach space and B(X)be the set of all bounded linear operators on X.Suppose that α is an automoy-phism on B(X).A linear mapping δ on B(X)is called an α-centralizable mapping at G if δ(G)=δ(A)α(B)=α(A)δ(B)for all A、B∈B(X)with AB=G.We say that an element G is an α-all centralizable point of B(X)if every α-centralizable mappingδat G is an α-centralizer.In this paper,we show that every α-centralizable mapping at nonzero element in B(X)is an α-all cen-tralizable point.
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