| *-代数上强保持新积的映射 |
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| 引用本文： | 张芳娟.*-代数上强保持新积的映射[J].山东大学学报(理学版),2019,54(12):46-49. |
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| 作者姓名： | 张芳娟 |
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| 作者单位： | 西安邮电大学理学院, 陕西 西安 710121 |
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| 基金项目： | 国家自然科学基金资助项目(11601420);陕西省自然科学基础研究计划资助项目(2018JM1053) |
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| 摘 要： | 设R是有单位元的*-代数,若R包含非平凡对称幂等元P满足:(1)若ARP={0},则A=0;(2)若AR(I-P)={0},则A=0。设φ:R→R是满射,则φ强保持新积当且仅当存在Z∈ZS(R)且Z2=I,使得对所有X∈R, 有φ(X)=ZX。作为应用,在没有I1型的中心直和项的von Neumann代数上和素*-环上得到相似的结果。
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| 关 键 词： | 新积 保持映射 *-代数 |
Strong new product preserving maps on *-algebras |
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| ZHANG Fang-juan.Strong new product preserving maps on *-algebras[J].Journal of Shandong University,2019,54(12):46-49. |
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| Authors: | ZHANG Fang-juan |
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| Institution: | School of Science, Xian University of Posts and Telecommunications, Xian 710121, Shaanxi, China |
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| Abstract: | Let R be a unital *-algebra with a nontrivial symmetric idempotent P which satisfies:(1)ARP={0} implies A=0;(2)AR(I-P)={0} implies A=0. Let φ:R→R be a surjective map. Then φ is strong new product preserving if and only if there exists an element Z∈ZS(R)with Z2=I such that φ(X)=ZX for all X∈R. As an application, a characterization of strong new product preserving on von Neumann algebras with no central summands of type I1 and prime *-ring are obtained. |
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| Keywords: | new product preserving map *-algebra |
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