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改进的Tsirelson空间TM上的Wigner定理
Wigner's Theorem on the Modified Tsirelson Space TM
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TM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TM上的Wigner型定理.
Let X and Y be normed space. We say that a map f:X→Y is a phaseisometry if it satisfies {||f(x) + f(y)||,||f(x)-f(y)||}={||x + y||,||x-y||} (x, y ∈ X). Suppose that g, f:X→Y are maps. If there is a phase function ε:X→{-1, 1} such that ε·f=g, then we say that f is phase-equivalent to g. We shall prove that every phase-isometry between two modified Tsirelson spaces TM is phase-equivalent to a linear isometry. This can be considered as a new version of the famous Wigner's theorem for the modified Tsirelson space TM.
改进的Tsirelson空间TM / 相位等价 / 线性等距 / Wigner定理 {{custom_keyword}} /
modified Tsirelson space TM / phase equivalent / linear isometries / Wigner's theorem {{custom_keyword}} /
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国家自然科学基金资助项目（11371201）
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