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].
2
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
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.
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.