Homogeneous families on trees and subsymmetric basic sequences

DOI10.1016/J.AIM.2018.06.008arXiv1607.06135WikidataQ111288302 ScholiaQ111288302MaRDI QIDQ6275787

Author name not available (Why is that?)

Publication date: 20 July 2016

Abstract: We study density requirements on a given Banach space that guarantee the existence of subsymmetric basic sequences by extending Tsirelson's well-known space to larger index sets. We prove that for every cardinal $kappa$ smaller than the first Mahlo cardinal there is a reflexive Banach space of density $kappa$ without subsymmetric basic sequences. As for Tsirelson's space, our construction is based on the existence of a rich collection of homogeneous families on large index sets for which one can estimate the complexity on any given infinite set. This is used to describe detailedly the asymptotic structure of the spaces. The collections of families are of independent interest and their existence is proved inductively. The fundamental stepping up argument is the analysis of such collections of families on trees.

Mathematics Subject Classification ID

No records found.

This page was built for publication: Homogeneous families on trees and subsymmetric basic sequences

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6275787)