A geometry characteristic of Banach spaces with c 1-norm
详细信息 查看全文
- 作者：Jipu Ma (1)
- 关键词：Banach space ; geometry ; non ; linear analysis ; global analysis ; 46T20 ; 54E99 ; 58B20
- 刊名：Frontiers of Mathematics in China
- 出版年：2014
- 出版时间：October 2014
- 年：2014
- 卷：9
- 期：5
- 页码：1089-1103
- 全文大小：238 KB
- 参考文献：1. Abraham R, Marsden J E, Ratiu T. Manifold, Tensor Analysis and Its Applications. New York: Springer-Verlag, 1988 4612-1029-0" target="_blank" title="It opens in new window">CrossRef
2. Ma Jipu. A generalized preimage theorem in global analysis. Sci China Ser A, 2001, 44(3): 299-03 CrossRef
3. Ma Jipu. Three classes of smooth Banach manifolds in / B( / E,F). Sci China Ser A, 2007, 50(9): 1233-239 CrossRef
4. Ma Jipu. A generalized transversality in global analysis. Pacific J Math, 2008, 236(2): 357-71 CrossRef
5. Ma Jipu. Complete rank theorem of advanced calculus and singularities of bounded linear operators. Front Math China, 2008, 3(2): 304-16 464-008-0019-8" target="_blank" title="It opens in new window">CrossRef
6. Nashed M Z. Generalized Inverses and Applications. New York, San-Francisco, London: Academic Press, 1976
7. Zeidler E. Nonlinear Functional Analysis and Its Applications IV. New York-Berlin: Springer-Verlag, 1988 4612-4566-7" target="_blank" title="It opens in new window">CrossRef - 作者单位：Jipu Ma (1)
1. Department of Mathematics, Nanjing University, Nanjing, 210093, China - ISSN：1673-3576
文摘
Let E be a Banach space with the c 1-norm ‖·-in E\{0}, and let S(E) = {e ?E: -em class="a-plus-plus">e-= 1}. In this paper, a geometry characteristic for E is presented by using a geometrical construct of S(E). That is, the following theorem holds: the norm of E is of c 1 in E\{0} if and only if S(E) is a c 1 submanifold of E, with codimS(E) = 1. The theorem is very clear, however, its proof is non-trivial, which shows an intrinsic connection between the continuous differentiability of the norm ‖·-in E\{0} and differential structure of S(E).