改进的Tsirelson空间TM上的Wigner定理

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改进的Tsirelson空间T_M上的Wigner定理

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改进的Tsirelson空间T_M上的Wigner定理熊晓蕾, 谭冬妮天津理工大学数学系天津 300384 Wigner's Theorem on the Modified Tsirelson Space T_M Xiao Lei XIONG, Dong Ni TANDepartment of Mathematics, Tianjin University of Technology, Tianjin 300384, P. R. China

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摘要设X和Y是赋范空间，如果映射f：X→Y满足{||f（x）+f（y）||，||f（x）-f（y）||}={||x+y||，||x-y||}（x，y∈X），则称f是一个相位等距算子.设g，f：X→Y是映射，若存在相位函数ε：X→{-1，1}，使得ε·f=g，则称g和f是相位等价的.本文将证明改进的Tsirelson空间T_M上的任意满相位等距算子均相位等价于一个线性等距算子.该结论同时也给出了改进的Tsirelson空间T_M上的Wigner型定理.

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收稿日期: 2019-09-28

MR (2010):

O177.2

基金资助:国家自然科学基金资助项目（11371201）

通讯作者:谭冬妮E-mail: tandongni0608@sina.cn

作者简介: 熊晓蕾,E-mail:x719179931@163.com

引用本文:

熊晓蕾, 谭冬妮. 改进的Tsirelson空间T_M上的Wigner定理[J]. 数学学报, 2020, 63(6): 629-638. Xiao Lei XIONG, Dong Ni TAN. Wigner's Theorem on the Modified Tsirelson Space T_M. Acta Mathematica Sinica, Chinese Series, 2020, 63(6): 629-638.

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