2005/02/02 by Valentin Ferenczi, Ferenczi, Valentin
Mathematics · #46B03 #46B15 #Advanced Banach Space Theory #Advanced Topics in Algebra #Approximation Theory and Sequence Spaces #Combinatorics (math.CO) #FOS: Mathematics #Functional Analysis (math.FA) #math.CO #math.FA #msc:46B03 #msc:46B15
paper · pdf · doi:10.48550/arxiv.math/0502054
openalex publication_date 2005/02/02 · arxiv created 2005/02/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If a Banach space is saturated with basic sequences whose linear span embeds into the linear span of any subsequence, then it contains a minimal subspace. It follows that any Banach space is either ergodic or contains a minimal subspace. For a Banach space X with an (unconditional) basis, topological 0-1 law type dichotomies are stated for block-subspaces of X as well as for subspaces of X with a successive FDD on its basis. A uniformity principle for properties of block-sequences, results about block-homogeneity, and a possible method to construct a Banach space with an unconditional basis, which has a complemented subspace without an unconditional basis, are deduced.