| K-POTENT PRESERVING LINEAR MAPS |
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| 引用本文： | 侯绳照,侯晋川. K-POTENT PRESERVING LINEAR MAPS[J]. 数学物理学报(B辑英文版), 2002, 22(4): 517-525. DOI: 10.1016/S0252-9602(17)30326-0 |
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| 作者姓名： | 侯绳照 侯晋川 |
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| 作者单位： | Hou Shengzhao Hou JinchuanDepartment of Mathematics，Shanxi Teachers University，Linfen 041004，China |
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| 基金项目： | The project is partially supported by NNSFC and PNSFS |
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| 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 φ a weakly continuous linear surjective map from B(X) into itself. It is shown that φ 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 λ satisfying λk-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 multiplied by an invertible element with (k - l)-th power I.
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| 收稿时间： | 2000-01-31 |
K-POTENT PRESERVING LINEAR MAPS |
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| Hou Shengzhao Hou Jinchuan. K-POTENT PRESERVING LINEAR MAPS[J]. Acta Mathematica Scientia, 2002, 22(4): 517-525. DOI: 10.1016/S0252-9602(17)30326-0 |
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| Authors: | Hou Shengzhao Hou Jinchuan |
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| Affiliation: | Hou Shengzhao Hou JinchuanDepartment of Mathematics,Shanxi Teachers University,Linfen 041004,China |
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| Abstract: | Let B(X) be the Banach algebra of all bounded linear operators on a complcx Banach space X. Let k ≥ 2 be an integer and φ a weakly continuous linear surjective map from B(X) into itself. It is shown that φ 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 λ satisfying λk-1 = 1. Let A be avon Neumann algebra andB 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 multiplied by an invertible element with (k - 1)-th power I. |
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| Keywords: | Banach space operator k-potent operator automorphism |
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