ALp -空间的单位球面上Lipschitz映射的等距延拓

数学物理学报 ›› 2012, Vol. 32 ›› Issue (2): 387-394.

AL_p -空间的单位球面上Lipschitz映射的等距延拓

高金梅¹|谭冬妮²

1.青岛大学数学科学学院山东青岛 260071|
2.天津理工大学数学系天津 300071

收稿日期:2010-11-25 修回日期:2011-12-30 出版日期:2012-04-25 发布日期:2012-04-25
基金资助:
教育部博士点基金(20060055010)和国家自然科学基金 (41171183)资助

On Extension of Isometries Between Unit Spheres in AL_p-spaces (1<p<∞)

GAO Jin-Mei¹, TAN Dong-Ni²

1.School of Mathematics, Qingdao University, Shandong Qingdao 266071;
2.School of Mathematics, Tianjin University of Technology, Tianjin 300071

Received:2010-11-25 Revised:2011-12-30 Online:2012-04-25 Published:2012-04-25
Supported by:
教育部博士点基金(20060055010)和国家自然科学基金 (41171183)资助

摘要/Abstract

摘要：

该文研究了L^p(Ω, ∑, μ; L^q(X, A, ν)) (2≤q<p<∞) 单位球面之间的1-Lipschitz映射以及L^p (Ω, ∑, μ; L^q(X, A, ν))(1<p<≤2) 单位球面之间的反-1-Lipschitz映射, 并证明了该映射可以延拓成为全空间上的实线性等距映射.

关键词: 等距延拓, 1-Lipschitz 映射, 严格凸赋范空间, Bochner 积分

Abstract:

In this paper, we discuss the 1-Lipschitz mappings between the unit spheres in vector valued spaces L^p(Ω, ∑, μ; L^q(X, A, ν)) (2≤q<p<∞) and anti-1-Lipschitz mappings between the unit spheres in vector valued spaces L^p (Ω, ∑, μ; L^q(X, A, ν))(1<p<≤2), and obtain that every such mapping can be extended to be a real linear isometry on the whole space L^p(Ω, ∑, μ; L^q(X, A, ν)).

中图分类号:

46B04

高金梅, 谭冬妮. AL_p -空间的单位球面上Lipschitz映射的等距延拓[J]. 数学物理学报, 2012, 32(2): 387-394.

GAO Jin-Mei, TAN Dong-Ni. On Extension of Isometries Between Unit Spheres in AL_p-spaces (1<p<∞)[J]. Acta mathematica scientia,Series A, 2012, 32(2): 387-394.

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