On the unconditional subsequence property

Authors

Edward Odell, The University of Texas at Austin
Bentuo Zheng, The University of Texas at AustinFollow

Abstract

We show that a construction of Johnson, Maurey and Schechtman leads to the existence of a weakly null sequence (fi) in (∑ Lpi)ℓ2, where pi ↓ 1, so that for all ε > 0 and 1 < q ≤ 2, every subsequence of (fi) admits a block basis (1 + ε)-equivalent to the Haar basis for Lq. We give an example of a reflexive Banach space having the unconditional subsequence property but not uniformly so.

Publication Title

Journal of Functional Analysis

Recommended Citation

Odell, E., & Zheng, B. (2010). On the unconditional subsequence property. Journal of Functional Analysis, 258 (2), 604-615. https://doi.org/10.1016/j.jfa.2009.07.015