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Israel Journal of Mathematics

, Volume 143, Issue 1, pp 223–238 | Cite as

1-spreading models in mixed Tsirelson spacemodels in mixed Tsirelson space

  • Denny H. Leung
  • Wee-Kee Tang
Article

Abstract

Suppose that (F n ) n=1 is a sequence of regular families of finite subsets of ℝ and (θ n ) n=1 is a nonincreasing null sequence in (0,1). The mixed Tsirelson spaceT[(θ n ,F n ) n=1 ] is the completion ofc 00 with respect to the implicitly defined norm\(\left\| x \right\| = \max \{ \left\| x \right\|_{c_0 ,} \mathop {\sup }\limits_n \user2{sup}\theta _n \sum\limits_{i = 1}^k {\left\| {E_i x} \right\|} \} \), where the last supremum is taken over all sequences (E i ) i=1 k in [ℕ]<∞ such that maxE i<minE i +1 and\(\left\{ {\min E_i :1 \leqslant i \leqslant k} \right\} \in \mathcal{F}_n \). Necessary and sufficient conditions are obtained for the existence of higher order ℓ1-spreading models in every subspace generated by a subsequence of the unit vector basis ofT[(θ n ,F n ) n=1 ].

Keywords

Banach Space American Mathematical Society Block Basis Finite Subset Unit Vector Basis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University 2004

Authors and Affiliations

  • Denny H. Leung
    • 1
  • Wee-Kee Tang
    • 2
  1. 1.Department of MathematicsNational University of SingaporeSingapore
  2. 2.Mathematics and Mathematics Education, National Institute of EducationNanyang Technological UniversitySingapore

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