The Characterization Of Uniformly Eberlein Compact Sets In C₀(?)

In 1985,Argyros and Farmaki gave a topological characterization of uniformly Eberlein compact sets in c0(?),that is,a non-empty weakly compact set K?c0(?)is uniformly Eberlein compact if and only if for any ?>0,there is a decomposition ?={?m(?):m?N}and a sequence of natural numbers {k(m,?):m ?N} so that for ?x?K and ?m?N satisfying card{???m(?):|x(?)|>?}?k(m,?).Recently,Professor L.Cheng?Lancient and Raja have proved that the super weakly compact set is uniformly Eberlein compact by proving that the closed convex hull of a super weakly compact set is still a super weakly compact set.Motivated by the above two theorems,this thesis obtains the characterization of uniformly Eberlein compact sets in c0(?)by discussing in two cases through construction and Grothendiek-type theorem,that is,a non-empty weakly compact set K ?c0(?)is uniformly Eberlein compact if and only if K is a subset of the direct sum of countable pairwise disjoint super weakly compact sets.