| 赋β-范空间中单位球面间的等距算子的线性延拓 |
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| 引用本文： | 杨秀忠,侯志彬,傅小红. 赋β-范空间中单位球面间的等距算子的线性延拓[J]. 数学学报, 2005, 48(6): 1199-1202. DOI: cnki:ISSN:0583-1431.0.2005-06-020 |
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| 作者姓名： | 杨秀忠 侯志彬 傅小红 |
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| 作者单位： | [1]南开大学数学科学学院,天津300071 [2]河北师大数学系,石家庄050016 |
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| 基金项目： | 国家自然科学基金资助项目（10271060）;高校博士点基金资助项目（20010055013） |
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| 摘 要： | 本文得到了等距映射的线性延拓的一般结果:设E,F是赋范(或β-严格凸赋β-范)线性空间,若V_0:S_1(E)→S_1(F)是等距,且对任意的x,y∈S_1(E),有‖V_0x-|(?)|V_0y‖≤‖x-|(?)|y‖,(?)∈R,则V_0必可延拓到全空间上等距算子(或线性等距算子)。特别,当E,F是赋范线性空间,V_0是满射或F为严格凸空间时,则V_0必可延拓为全空间的线性等距算子,从而推广了文[3～5]中的相应结果。
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| 关 键 词： | 等距映射 等距延拓 Tingley问题 |
| 文章编号： | 0583-1431（2005）06-1199-04 |
| 收稿时间： | 2005-04-15 |
| 修稿时间： | 2005-04-152005-08-23 |
On Linear Extension of Isometries Between the Unit Spheres of β-Normed Spaces |
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| Xiu Zhong YANG ,Zhi Bin HOU, Xiao Hong FU. On Linear Extension of Isometries Between the Unit Spheres of β-Normed Spaces[J]. Acta Mathematica Sinica, 2005, 48(6): 1199-1202. DOI: cnki:ISSN:0583-1431.0.2005-06-020 |
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| Authors: | Xiu Zhong YANG Zhi Bin HOU Xiao Hong FU |
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| Affiliation: | 1 School of Mathematical Sciedees, Nankai University, Tianjin, 300071, P. R. China ;2 Department of Mathematics, Hebei Normal University, Shijiazhuang, 050016, P. R. China |
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| Abstract: | In this paper, we obtain the general results on extension of isometries: Let E, F be normed (or β-strictly convex β-normed) spaces. If V_0: S_1(E)→S_1 (F) is an isometry and for all x, y∈S_1(E) we have ‖V_0x-|λ|V_0y‖≤‖x-|λ|y‖, (?)λ∈R, then V_0 can be extended to be an isometry (or linear isometry) on the whole space. In particular, if E, F are a normed spaces, V_0 is surjective or F is strictly convex, then V_0 can be extended to be a linear isometry on the whole space, thus generalizing the corresponding results in [3-5]. |
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| Keywords: | Isometry Extension of isometry Tingley problem |
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