保持算子Jordan-?-triple乘积幂等性的映射

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英文篇名：Mappings Preserving the Idempotency of Jordan-?-triple Product of Operators 作者：董改芳 英文作者：DONG Gaifang;Shuozhou Advanced Normal College; 关键词：不定内积空间 ; 幂等性 ; 算子Jordan-?-triple乘积 ; 算子Jordan-*-triple乘积 英文关键词：indefinite inner product spaces;;idempotency;;Jordan ? triple product of operators;;Jordan-*-triple product of operators 中文刊名：SJYX 英文刊名：Journal of Taiyuan Normal University(Natural Science Edition) 机构：朔州师范高等专科学校; 出版日期：2019-06-25 出版单位：太原师范学院学报(自然科学版) 年：2019 期：v.18;No.68 语种：中文; 页：SJYX201902007 页数：6 CN：02 ISSN：14-1304/N 分类号：26-31

摘要

设H是无限维的复的完备的不定内积空间,B(H)是H上所有有界线性算子构成的代数,ΩB(H).本文主要刻画Ω上保持算子Jordan-?-triple乘积幂等性的映射.当H为Hilbert空间时,作为推论,给出了Ω上保持算子Jordan-*-triple乘积幂等性的映射的具体形式.
        Let H be a infinite complex completely indefinite inner product spaces,Let B(H)be the sets of all linear operators on H.LetΩbe a subset of B(H),which containing at least all nonzero scalar multiples of rank-one idempotents and I.The maps preserving the idempotency of Jordan-?-triple product of operators onΩare characterized.Consequently,if H is a Hilbert spaces,the maps preserving the idempotency of Jordan-*-triple product of operators onΩare completely classified.

引文

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