期刊论文详细信息
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 卷:363 |
A note on extension of isometric embedding from a Banach space E into the universal space l∞(Γ) | |
Article | |
Liu, Rui1,2,3  | |
[1] Nankai Univ, Dept Math, Tianjin 300071, Peoples R China | |
[2] Nankai Univ, LPMC, Tianjin 300071, Peoples R China | |
[3] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA | |
关键词: Isometric embedding; Unit sphere; Universal space; | |
DOI : 10.1016/j.jmaa.2009.08.033 | |
来源: Elsevier | |
【 摘 要 】
In this paper we shall present a short proof on the extension problem of isometric embedding between unit spheres of a Banach space E and the universal space l(infinity)(Gamma). We prove that, under some condition, every isometric embedding from S(E) into S(l(infinity)(Gamma)) can be positive-homogeneously isometrically extended to the whole space. Since every Banach space E is isometric to a subspace of l(infinity)(S(E*)), isometric extension problems on a class of atomic AM-spaces is solved. (C) 2009 Elsevier Inc. All rights reserved.
【 授权许可】
Free
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