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| Author: |
許勝溢 Shen-Yi Hsu |
|---|---|
| Thesis Title: |
Hahn-Banach定理, Fritz John楕球定理及範數表現定理 Hahn-Banach extension theorem, Fritz John's ellipsoid theorem and representation of norms |
| Advisor: |
施茂祥
Shih, Mau-Hsiang |
| Degree: |
碩士 Master |
| Department: |
數學系 Department of Mathematics |
| Thesis Publication Year: | 2007 |
| Academic Year: | 95 |
| Language: | 英文 |
| Number of pages: | 8 |
| Keywords (in English): | F. John ellipsoid theorem |
| Thesis Type: | Academic thesis/ dissertation |
| Reference times: | Clicks: 274 Downloads: 11 |
| Share: |
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在n維歐氏空間中, 一個緊緻凸的對稱集, 會被包含在唯一一個體積最小的楕球中, 而此楕球若縮小n的平方根分之一倍, 則反而會被包含在原本的對稱集內. 同樣條件的集合, 也可以表成所有以原點為中心的楕球的交集. 以上敘述幾何直觀顯得顯然, 本論文利用Hahn-Banach定理提供一嚴謹證明.
[AS] T. Ando and M. H. Shih: Simultaneous contractibility, SIAM J. Matrix Anal. Appl. Vol.19. No. 2, pp. 487-498, April 1998.
[Jo] F. John: Extremum problems with inequalities as subsidiary conditions, reprinted in Collected Papers, Vol. 2, pp. 543-560, J. Moser, ed., Birkh¨auser, Boston, MA, 1985.
[HJ] R. A. Horn and C. R. Johnson: “Matrix Analysis,” Cambridge University Press, Cambridge, 1985.
[Ru] W. Rudin: “Functional Analysis,” 2nd ed., McGraw-Hill Companies, Inc., Bosten, 1991.
