| In this paper,we mainly study the Markushevich basis of super-weakly compactly generated space and the dual unit ball of its closed subspace by using the techniques of PRI and transfinite induction.We all know that a Banach spacce is weakly compactly generated if and only if it admits a(σ-)weakly compact Markushevich basis.Based on the fact that all weakly closed subsets of a super-weakly compact set are super-weakly compact set,we show that a Banach space is generated by a super-weakly compact set if and only if it admits a super-weakly compact Markushevich basis.On the other hand,motivated by the result of M.Fabian,V.Montesinos and V.Zizler in 2005 that the Banach space X is a subspace of a weakly compact generated space if and only if its dual unit ball Bx*is an Eberlein compact set in w*tpology,we proved that Banach space X is a subspace of the super-weakly compact generated space if and only if the dual unit ball Bx*of X,in its w*tpology,is an uniformly Eberlein compact set. |
