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The Quarterly Journal of Mathematics Advance Access published online on September 29, 2007
The Quarterly Journal of Mathematics, doi:10.1093/qmath/ham026
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© The author 2007. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

On the Structure of Asymptotic lp Spaces

E. Odell{dagger}, TH. Schlumprecht {ddagger} and A. Zsák §

Department of Mathematics, University of Texas, 1 University Station, C1200 Austin, TX 78712, USA
Department of Mathematics, Texas A&M University, College Station, TX 78712, USA
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK

{dagger} Corresponding author. E-mail: odell{at}math.utexas.edu

Received 9 March 2007;
  Abstract

We prove that if X is a separable, reflexive space which is asymptotic lp for some 1 ≤ p ≤ {infty}, then X embeds into a reflexive space Z having an asymptotic lp finite-dimensional decomposition (FDD). This result leads to an intrinsic characterization of subspaces of spaces with an asymptotic lp FDD. More general results of this type are also obtained. As a consequence, we prove the existence of universal spaces for certain classes of separable, reflexive and asymptotic lp spaces.

{ddagger} E-mail: schlump{at}math.tamu.edu

§ E-mail: andras.zsak{at}maths.nottingham.ac.uk


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