数学物理学报(英文版) ›› 2002, Vol. 22 ›› Issue (4): 517-525.
侯绳照, 侯晋川
HOU Sheng-Zhao, HOU Jin-Chuan
摘要：
Let B(X) be the Banach algebra of all bounded linear operators on a complex Banach space X. Let k 2 be an integer and a weakly continuous linear surjective map from B(X) into itself. It is shown that is k-potent preserving if and only if it is k-th-power preserving, and in turn, if and only if it is either an automorphism or an antiautomorphism on B(X) multiplied by a complex number satisfying k−1 = 1. Let A be a von Neumann
algebra and B be a Banach algebra, it is also shown that a bounded surjective linear map from A onto B is k-potent preserving if and only if it is a Jordan homomorphism multipliedby an invertible element with (k − 1)-th power I.
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