Some Converses of the Strong Separation Theorem
碩士 === 國立中山大學 === 應用數學研究所 === 81 === A convex set B in a real locally convex space X is said to have the separation property if it can be separated from any closed convex set A in X, which is disjoint from B, by a closed hyperplane. The st...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Others |
| Language: | en_US |
| Published: |
1993
|
| Online Access: | http://ndltd.ncl.edu.tw/handle/61038108976946444971 |
| Summary: | 碩士 === 國立中山大學 === 應用數學研究所 === 81 === A convex set B in a real locally convex space X is said to have
the separation property if it can be separated from any closed
convex set A in X, which is disjoint from B, by a closed
hyperplane. The strong separation theorem says that if B is
weakly compact then it has the separation property. In this
paper, we present several versions for the converse and discuss
some applications. For example, we proved that a normed space
is reflexive if and only if its closed unit ball has the
separation property. Results in this paper can be considered as
generalizations and supplements of the famous James' Theorem.
|
|---|