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The Quarterly Journal of Mathematics Advance Access published online on January 2, 2009
The Quarterly Journal of Mathematics, doi:10.1093/qmath/han036
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© The author 2008. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

ASYMPTOTIC UNCONDITIONALITY

S. R. Cowell {dagger} and N. J. Kalton{ddagger}

Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211, USA

{ddagger} Corresponding author. E-mail: nigel{at}math.missouri.edu

Received 16 September 2008;
  Abstract

We show that a separable real Banach space embeds almost isometrically in a space Y with a shrinking 1-unconditional basis if and only if lim n->{infty}|| x* + xn*|| = lim n->{infty}||x* – xn*|| whenever x* isin X*, Formula is a weak*-null sequence and both limits exist. If X is reflexive then Y can be assumed reflexive. These results provide the isometric counterparts of recent work of Johnson and Zheng.

{dagger} E-mail: simon{at}math.missouri.edu


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