2017/10/04 by Ryan M. Causey, Gilles Lancien, Causey, Ryan M. +1
Mathematics · #46B20 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.1710.01638
openalex publication_date 2017/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a previous work, the first named author described the set \cal P of all values of the Szlenk indices of separable Banach spaces. We complete this result by showing that for any integer n and any ordinal α in \cal P, there exists a separable Banach space X such that the Szlenk of the dual of order k of X is equal to the first infinite ordinal ω for all k in \0,..,n-1\ and equal to α for k=n. One of the ingredients is to show that the Lindenstrauss space and its dual both have a Szlenk index equal to ω. We also show that any element of \cal P can be realized as a Szlenk index of a reflexive Banach space with an unconditional basis.