Almost isometric constants for partial unconditionality

Causey, R.; Dilworth, S.

doi:10.1090/proc/13004

Almost isometric constants for partial unconditionality
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by R. M. Causey and S. J. Dilworth PDF

Proc. Amer. Math. Soc. 144 (2016), 3397-3404 Request permission

Abstract:

We discuss optimal constants of certain projections on subsequences of weakly null sequences. Positive results yield constants arbitrarily close to $1$ for Schreier type projections, and arbitrarily close to $1$ for Elton type projections under the assumption that the weakly null sequence admits no subsequence generating a $c_0$ spreading model. As an application, we prove that a weakly null sequence admitting a spreading model not equivalent to the $c_0$ basis has a quasi-greedy subsequence with quasi-greedy constant arbitrarily close to $1$.

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