摘要
We prove that a topological space is uniform Eberlein compact iff it is homeomorphic to a super weakly compact subset C of a Banach space such that the closed convex hull coC of C is super weakly compact. We also show that a Banach space X is super weakly compactly generated iff the dual unit ball B;of X;in its weak star topology is affinely homeomorphic to a super weakly compactly convex subset of a Banach space.
We prove that a topological space is uniform Eberlein compact iff it is homeomorphic to a super weakly compact subset C of a Banach space such that the closed convex hull coC of C is super weakly compact. We also show that a Banach space X is super weakly compactly generated iff the dual unit ball B_(X~*) of X~* in its weak star topology is affinely homeomorphic to a super weakly compactly convex subset of a Banach space.
基金
The first author is supported by Natural Science Foundation of Guangxi Education Department(Grant No.KY2015LX518)
the second author is supported by National Natural Science Foundation of China(Grant No.11671065)
the third author is supported by National Natural Science Foundation of China(Grant No.11471271)
