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Banach spaces of bounded Szlenk index

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Odell E., Schlumprecht T., Zsák A.

Studia Mathematica

2007

tom 183

nr 1

63-97

For a countable ordinal α we denote by $𝓒_{α}$ the class of separable, reflexive Banach spaces whose Szlenk index and the Szlenk index of their dual are bounded by α. We show that each $𝓒_{α}$ admits a separable, reflexive universal space. We also show that spaces in the class $𝓒_{ω^{α·ω}}$ embed into spaces of the same class with a basis. As a consequence we deduce that each $𝓒_{α}$ is analytic in the Effros-Borel structure of subspaces of C[0,1].

Banach spaces of bounded Szlenk index II

100%

Freeman D., Odell E., Schlumprecht T., Zsák A.

Fundamenta Mathematicae

2009

tom 205

nr 2

161-177

For every α < ω₁ we establish the existence of a separable Banach space whose Szlenk index is $ω^{αω+1}$ and which is universal for all separable Banach spaces whose Szlenk index does not exceed $ω^{αω}$. In order to prove that result we provide an intrinsic characterization of which Banach spaces embed into a space admitting an FDD with Tsirelson type upper estimates.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Studia Mathematica

2 Odell E.

2 Schlumprecht T.

2 Zsák A.

1 Freeman D.

1 2009

1 2007

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Banach spaces of bounded Szlenk index

Banach spaces of bounded Szlenk index II