标题： B(X)上李可交换映射的特征 显示英文标题

标题： Characterization of Lie centralizable mappings on B(X)

摘要： 假设B(X)是复Banach空间X上所有有界线性算子的代数，令W属于B(X)，使得cl(W(X))不等于X或者W=zI，其中z是复数，I是单位算子。我们证明，如果f:B(X)→B(X)是一个在W处Lie中心化的加法映射，则对于所有A属于B(X)，有f(A)=kA+h(A)，其中k是复数，h:B(X)→CI是一个加法映射，使得对于所有满足AB=W的A,B属于B(X)，有h([A,B])=0。 显示英文摘要

摘要： Assume that B(X) is the algebra of all bounded linear operators on a complex Banach space X, and let W in B(X) is such that cl(W(X)) is not equal to X or W=zI, where z is a complex number and I is the identity operator. We show that if f: B(X) --> B(X) is an additive mapping Lie centralizable at W, then f(A)=kA+h(A) for all A in B(X), where k is a complex number and h:B(X)--> CI is an additive mapping such that h([A,B])=0 for all A,B in B(X) with AB=W.