复l^(∞)(Γ,H)空间单位球面的相位等距延拓问题  

Extension problem of phase-isometries between the unit spheres of complex l^(∞)(Γ,H)space

作　　者：杜金尚 赵君灵 宋眉眉[1] DU Jinshang;ZHAO Junling;SONG Meimei(School of Science,Tianjin University of Technology,Tianjin 300384,China)

机构地区：[1]天津理工大学理学院,天津300384

出　　处：《天津理工大学学报》2024年第2期120-126,共7页Journal of Tianjin University of Technology

基　　金：国家自然科学基金(11971348)。

摘　　要：针对一个结合Wigner定理与Tingley问题的新型问题,假设f:S_(X)→S_(Y)是在赋范空间单位球面上的满映射,且该映射是相位等距算子,则该映射的正齐次延拓相位是否等价于一个实线性等距算子?在复l^(∞)(Γ,H)空间单位球面上进行相关证明。研究方法是以实l^(∞)(Γ,H)空间上的Wigner型定理与复l^(∞)(Γ)空间单位球面上的相位等距延拓的结论为基础,研究在复数空间上的不同情况。得到以下结论:复l^(∞)(Γ,H)空间单位球面上的映射可延拓成全空间上的满相位等距,且这个映射是相位等价于一个实线性等距映射。For a new problem combining Wigner’s theorem and Tingley’s problem,suppose that f:S_(X)→S_(Y) is a surjective mapping on the unit sphere of normed space,and the mapping is a phase isometry,then its positive homogeneous extension is a phase-isometry which is phase equivalent to a real linear isometry?This paper answers the question on the unit sphere of complexl^(∞)(Γ,H)space.The research method is based on the Wigner type theorem in reall^(∞)(Γ,H)space and the conclusion of phase isometric continuation on the unit sphere in complexl^(∞)(Γ)space.It is concluded that the mapping on the unit sphere of the complexl^(∞)(Γ,H)space can be extended to the surjective phase-isometry on the whole space,and the phase-isometry is equivalent to a real linear isometry.

关 键 词：Wigner定理 复l^(∞)(Γ H)空间 TINGLEY问题 MAZUR-ULAM定理 

分 类 号：O177[理学—数学]