On subspaces whose weak* derived sets are proper and norm dense

Abstract

We study long chains of iterated weak* derived sets, that is, sets of all weak* limits of bounded nets, of subspaces with the additional property that the penultimate weak* derived set is a proper norm dense subspace of the dual. We extend the result of Ostrovskii and show that in the dual of any non-quasi-reflexive Banach space containing an infinite-dimensional subspace with separable dual, we can find for any countable successor ordinal alpha a subspace whose weak* derived set of order alpha is proper and norm dense.

Keywords

• weak* derived set
• weak* sequential closure