On a generalized Mazur-Ulam question: Extension of isometries between unit spheres of Banach spaces

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	On a generalized Mazur-Ulam question: Extension of isometries between unit spheres of Banach spaces
	Cheng, L. X. ; Dong, Y. B. ; Cheng LX(程立新)
刊名	http://dx.doi.org/10.1016/j.jmaa.2010.11.025
	2011-05-15
关键词	DIFFERENTIABILITY POINTS
英文摘要	Natural Science Foundation of China [10771175, 11071201, 11001231]; We call a Banach space X admitting the Mazur-Ulam property (MUP) provided that for any Banach space Y, if f is an onto isometry between the two unit spheres of X and V. then it is the restriction of a linear isometry between the two spaces. A generalized Mazur-Ulam question is whether every Banach space admits the MUP. In this paper, we show first that the question has an affirmative answer for a general class of Banach spaces, namely, somewhere-flat spaces. As their immediate consequences, we obtain on the one hand that the question has an approximately positive answer: Given epsilon > 0, every Banach space X admits a (1 + epsilon)-equivalent norm such that X has the MUP; on the other hand, polyhedral spaces, CL-spaces admitting a smooth point (in particular, separable CL-spaces) have the MUP. (C) 2010 Elsevier Inc. All rights reserved.
语种	英语
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/66528]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Cheng, L. X.,Dong, Y. B.,Cheng LX. On a generalized Mazur-Ulam question: Extension of isometries between unit spheres of Banach spaces[J]. http://dx.doi.org/10.1016/j.jmaa.2010.11.025,2011.
APA	Cheng, L. X.,Dong, Y. B.,&程立新.(2011).On a generalized Mazur-Ulam question: Extension of isometries between unit spheres of Banach spaces.http://dx.doi.org/10.1016/j.jmaa.2010.11.025.
MLA	Cheng, L. X.,et al."On a generalized Mazur-Ulam question: Extension of isometries between unit spheres of Banach spaces".http://dx.doi.org/10.1016/j.jmaa.2010.11.025 (2011).