Extracting long basic sequences from systems of dispersed vectors

2010/10/30 by Jarno Talponen, Talponen, Jarno
Mathematics · #46B20 #46B26 #46Bxx #46M40 #Advanced Banach Space Theory #Advanced Topology and Set Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.1011.0071

openalex publication_date 2010/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study Banach spaces satisfying some geometric or structural properties involving tightness of transfinite sequences of nested linear subspaces. These properties are much weaker than WCG and closely related to Corson's property (C). Given a transfinite sequence of normalized vectors, which is dispersed or null in some sense, we extract a subsequence which is a biorthogonal sequence, or even a weakly null monotone basic sequence, depending on the setting. The Separable Complementation Property is established for spaces with an M-basis under rather weak geometric properties. We also consider an analogy of the Baire Category Theorem for the lattice of closed linear subspaces.

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