Partial Unconditionality
S. J. Dilworth, Edward William Odell, Th. Schlumprecht, András Zsák · arXiv (Cornell University) · 2005
J. Elton proved that every normalized weakly null sequence in a Banach space admits a subsequence that is nearly unconditional which is a weak form of unconditionality. The notion of near-unconditionality is quantified by a constant $K(δ)$ depending on a parameter $δ\in (0,1]$. It is unknown if $\sup_{δ>0} K(δ) 0} K(δ) 0} K(δ) > 5/4$.