TY - JOUR
T1 - Some converses of the strong separation theorem
AU - Gau, Hwa Long
AU - Wong, Ngai Ching
PY - 1996
Y1 - 1996
N2 - A convex subset B of a real locally convex space X is said to have the separation property if it can be separated from every closed convex subset A of 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 two versions of the converse and discuss an application of them. For example, we prove 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 supplements of the famous theorem of James.
AB - A convex subset B of a real locally convex space X is said to have the separation property if it can be separated from every closed convex subset A of 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 two versions of the converse and discuss an application of them. For example, we prove 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 supplements of the famous theorem of James.
UR - http://www.scopus.com/inward/record.url?scp=21344461658&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-96-03343-6
DO - 10.1090/S0002-9939-96-03343-6
M3 - 期刊論文
AN - SCOPUS:21344461658
SN - 0002-9939
VL - 124
SP - 2443
EP - 2449
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 8
ER -