\ell ^1-spreading models in mixed Tsirelson space

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dc.creatorLeung, Denny H.
dc.creatorTang, Wee-Kee
dc.date2003-03-29
dc.date.accessioned2026-07-07T04:56:30Z
dc.date.available2026-07-07T04:56:30Z
dc.descriptionSuppose that (F_n)_{n=1}^{\infty} is a sequence of regular families of finite subsets of N and (θ_n)_{n=1}^{\infty} is a nonincreasing null sequence in (0,1). The mixed Tsirelson space T[(θ_{n}, F_n)_{n=1}^{\infty}] is the completion of $c_{00}$ with respect to the implicitly defined norm ||x|| = max{||x||_{c_0}, sup_n sup θ_n \sum_{i=1}^{j}||E_{i}x||}, where the last supremum is taken over all finite subsets E_{1},...,E_{j} of N such that E_1 < >... <E_j and {min E_1,...,min E_j} \in F_n. Necessary and sufficient conditions are obtained for the existence of higher order \ell ^1-spreading models in every subspace generated by a subsequence of the unit vector basis of T[(θ_{n}, F_n)_{n=1}^{\infty}.
dc.identifierhttps://arxiv.org/abs/math/0303375
dc.identifierhttp://arxiv.org/abs/math/0303375
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/66941
dc.subjectFunctional Analysis
dc.subject46B
dc.title\ell ^1-spreading models in mixed Tsirelson space
dc.typetext

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