| 算子代数上的Jordan初等映射(英文) |
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| 引用本文： | 安润玲,侯晋川.算子代数上的Jordan初等映射(英文)[J].数学进展,2012(1):63-72. |
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| 作者姓名： | 安润玲 侯晋川 |
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| 作者单位： | 太原理工大学数学系 |
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| 基金项目： | supported by Youth Funds of Shanxi(No.2009021002);NSFC(No.11001194 and No.10771157);Program for the Top Young Academic Leaders of Higher Learning Institutions of Shanxi(TYAL) |
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| 摘 要： | 给定两个环R,R’.对于满足一定条件的环R,本文证明了若M:R→R’,M*:R’→R为满射且对A,C∈R和B,D∈R’满足M（AM*（B）C+CM*（B）A）=M（A）BM（C）+M（C）BM（A）,M*（BM（A）D+DM（A）B）=M*（B）AM*（D）+M*（D）AM*（B）则M和M*是可加的;若R和R’分别包含单位I和I’,M（I）,M*（I’）可逆,则存在环同构N使得M（A）=N（A）M（I）,M*（B）=N-1（BM（I））.特别地,若R=R’为标准算子代数或Hilbert空间套代数,则M和M*可加且存在有界可逆的线性或共轭线性算子S和T使得M（A）=SAT,M*（B）=TBS或M（A）=TA*S,M*（B）=（SBT）*对任意的A,B∈R成立.
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| 关 键 词： | Jordan同构 Jordan初等映射 套代数 |
Jordan Elementary Map on Operator Algebras |
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| AN Runling,HOU Jinchuan.Jordan Elementary Map on Operator Algebras[J].Advances in Mathematics,2012(1):63-72. |
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| Authors: | AN Runling HOU Jinchuan |
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| Institution: | (**) (Department of Mathematics,Taiyuan University of Technology,Taiyuan,Shanxi,030024,P.R.China) |
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| Abstract: | Let R and R′be two rings.Under some mild assumptions on R,we show that, if maps M:R→R’ and M*:R’→R are surjective and satisfy M（AM*（B）C+CM*（B）A）=M（A）BM（C）+M（C）BM（A）,M*（BM（A）D+DM（A）B）=M*（B）AM*（D）+M*（D）AM*（B） for all A,C∈R and B,D∈R’,then both M and M* are additive.And if R and R’ have identity I and I’,respectively,and M（I）,M*（I’） are invertible,then there is a Jordan ring isomorphism N such that M（A） = N（A）M（I） and M*（B） = N-1（BM（I））.In particular,if R = R’ is a standard operator algebra,or a nest algebra on a Hilbert space,then we can conclude that both M and M* are additive,and M（A） = SAT,M*（B） = TBS or M（A） = TA*S,M*（B） =（SBT）*,where S and T are bounded invertible linear or conjugate linear operators. |
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| Keywords: | Jordan isomorphism Jordan elementary map nest algebra |
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