This is an announcement for the paper "Extracting long basic sequences from systems of dispersed vectors" by Jarno Talponen.
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.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B26, 46Bxx, 46M40
Remarks: 17 pages
Submitted from: talponen@cc.hut.fi
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1011.0071
or