Weak* closures and derived sets in dual Banach spaces

Original · EN

The main results of the paper: (1) The dual Banach space X* contains a linear subspace A⊂ X* such that the set A⁽¹⁾ of all limits of weak* convergent bounded nets in A is a proper norm-dense subset of X* if and only if X is a non-quasi-reflexive Banach space containing an infinite-dimensional subspace with separable dual. (2) Let X be a non-reflexive Banach space. Then there exists a convex subset A⊂ X* such that A⁽¹⁾≠ A* (the latter denotes the weak* closure of A). (3) Let X be a quasi-reflexive Banach space and A⊂ X* be an absolutely convex subset. Then A⁽¹⁾=A*.