P. A. Brooker

collaborators

2 papers

math.FA2012

Szlenk and $w^{*}$ -dentability indices of the Banach spaces $C ([0, α])$

Philip A. H. Brooker

Let $α$ be an infinite ordinal and $γ$ the unique ordinal satisfying $ω^{ω^{γ}} \leq α < ω^{ω^{γ + 1}}$ . We show that the Banach space $C ([0, α])$ of all continuous scalar-valued functi…

math.FA2012

Three-space property for asymptotically uniformly smooth renormings

P. A. H. Brooker, G. Lancien

We prove that if $Y$ is a closed subspace of a Banach space $X$ such that $Y$ and $X / Y$ admit an equivalent asymptotically uniformly smooth norm, then $X$ also admits an equivalent…

Szlenk and w∗-dentability indices of the Banach spaces C([0,α])

Three-space property for asymptotically uniformly smooth renormings

Szlenk and $w^{*}$ -dentability indices of the Banach spaces $C ([0, α])$