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Estimation of the Szlenk index of reflexive Banach spaces using generalized Baernstein spaces (1308.5416v1)
Published 25 Aug 2013 in math.FA
Abstract: For each ordinal $\alpha< \omega_1$, we prove the existence of a separable, reflexive Banach space with a basis and Szlenk index $\omega{\alpha+1}$ which is universal for the class of separable, reflexive Banach spaces $X$ such that the Szlenk indices $Sz(X), Sz(X*)$ do not exceed $\omega\alpha$.