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Total subspaces with long chains of nowhere norming weak$^*$ sequential closures

Mikhail I. Ostrovskii
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Abstract

If a separable Banach space $X$ is such that for some nonquasireflexive Banach space $Y$ there exists a surjective strictly singular operator $T:X\to Y$ then for every countable ordinal $\alpha $ the dual of $X$ contains a subspace whose weak$^*$ sequential closures of orders less than $\alpha $ are not norming over any infinite-dimensional subspace of $X$ and whose weak$^*$ sequential closure of order $\alpha +1$ coincides with $X^*$

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Mikhail I. Ostrovskii. 1993-03-29. Total subspaces with long chains of nowhere norming weak$^*$ sequential closures. https://arxiv.org/abs/math/9303206

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