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


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 ].


Banach Space American Mathematical Society Block Basis Finite Subset Unit Vector Basis 
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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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