Abstract
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 co̅C 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.
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Acknowledgements
The authors are particularly grateful to Professor Lixin Cheng for his constructive discussion and encouragement in our work.
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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)
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Yang, Z.T., Lu, Y.F. & Cheng, Q.J. Super weak compactness and uniform Eberlein compacta. Acta. Math. Sin.-English Ser. 33, 545–553 (2017). https://doi.org/10.1007/s10114-017-6354-5
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DOI: https://doi.org/10.1007/s10114-017-6354-5