套代数上的一类非线性中心化子  

A class of nonlinear centralizers on nest algebras

作　　者：纪玉德[1] 吴冰 杨翠[2] JI Yude;WU Bing;YANG Cui(School of Sciences,Hebei University of Science and Technology,Shijiazhuang,Hebei 050018,China;School of Engineering Management,Hebei Polytechnic Institute,Shijiazhuang,Hebei 050091,China)

机构地区：[1]河北科技大学理学院,河北石家庄050018 [2]河北工程技术学院工程管理学院,河北石家庄050091

出　　处：《河北科技大学学报》2024年第2期176-180,共5页Journal of Hebei University of Science and Technology

基　　金：国家自然科学基金(61972093);河北省自然科学基金(F2022208007);河北省高等学校科学技术研究项目(ZD2022136)。

摘　　要：为了推广算子代数中的基本理论,对一类非线性映射成为套代数上的可加中心化子的条件进行了研究。首先,基于Hilbert空间上的非平凡套定义与该套有关的套代数,并定义套代数上的一个非线性映射;其次,采用矩阵分块方法获得关于此映射的几个性质;最后,证明套代数上满足某种条件的非线性映射为可加中心化子,给出刻画该映射的具体形式。结果表明,套代数上满足某种条件的非线性映射为可加中心化子,且可完全刻画。研究结果推广了非线性映射成为套代数上可加中心化子的结论,丰富了算子代数拓扑结构的分类问题,为套代数上其他类型非线性映射问题的刻画提供了借鉴与参考。In order to extend the basic theory of operator algebras,the conditions for a class of nonlinear mappings to become additive centralizers on nest algebras were studied.Firstly,the nest algebras related to a non-trivial nest based on a Hilbert space was defined,and a nonlinear mapping on the nest algebra was defined.Secondly,several properties about this mapping were obtained by using the matrix partitioning method.Finally,it was proved that a nonlinear mapping on the nest algebra that satisfies certain conditions was an additive centralizer,and a specific form for characterizing this mapping was provided.The results show that the nonlinear mapping satisfying some conditions on nested algebras is additive centralizer and can be characterized completely.The research results promote the conclusion that nonlinear mappings become additive centralizers on nested algebras,enrich the classification problem of topological structure for operator algebras,and provide reference and guidance for characterizing other types of nonlinear mappings on nested algebras.

关 键 词：算子代数 中心化子 非线性映射 HILBERT空间 矩阵分块 

分 类 号：O151.23[理学—数学]