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Almost isometric constants for partial unconditionality


Authors: R. M. Causey and S. J. Dilworth
Journal: Proc. Amer. Math. Soc. 144 (2016), 3397-3404
MSC (2010): Primary 46B15, 41A65
DOI: https://doi.org/10.1090/proc/13004
Published electronically: March 25, 2016
MathSciNet review: 3503707
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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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Additional Information

R. M. Causey
Affiliation: Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208
Email: causey@math.sc.edu

S. J. Dilworth
Affiliation: Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208
Email: dilworth@math.sc.edu

DOI: https://doi.org/10.1090/proc/13004
Received by editor(s): September 21, 2015
Published electronically: March 25, 2016
Additional Notes: The second author was supported by the National Science Foundation under Grant Number DMS-1361461
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2016 American Mathematical Society