### Weak closures and derived sets in dual Banach spaces

#### Abstract

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

DOI Code:
10.1285/i15900932v31n1p129

Keywords:
norming subspace ; quasi-reflexive Banach space ; total subspace ; weak$^*$ closure ; weak$^*$ derived set ; weak$^*$ sequential closure

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