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\ell^1-spreading models in subspaces of mixed Tsirelson spaces
Denny H. Leung, Wee-Kee Tang
We investigate the existence of higher order \ell^1-spreading models in subspaces of mixed Tsirelson spaces. For instance, we show that the following conditions are equivalent for…
\ell ^1-spreading models in mixed Tsirelson space
Denny H. Leung, Wee-Kee Tang
Suppose 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 s…
The Bourgain ell ^1-index of mixed Tsirelson space
Denny H. Leung, Wee-Kee Tang
Suppose that (F_n)_{n=0}^{\infty} is a sequence of regular families of finite subsets of N such that F_0 contains all singletons, and (θ_n)_{n=1}^{\infty} is a nonincreasing null s…
The -index of Tsirelson type spaces
Denny H. Leung, Wee-Kee Tang
If αand βare countable ordinals such that β\neq 0, denote by \tilde{T}_{α,β} the completion of with respect to the implicitly defined norm ||x|| = max{||x||_{c_{0}}, 1/2 s…
An asymptotic property of Schachermayer's space under renorming
Denka Kutzarova, Denny H. Leung
A Banach space X with closed unit ball B is said to have property 2-beta, repsectively 2-NUC if for every \ep > 0, there exists δ> 0 such that for every \ep-separated sequence (x_n…
On the complemented subspaces of the Schreier spaces
I. Gasparis, D. H. Leung
It is shown that the Schreier space X admits a set of continuum cardinality whose elements are mutually incomparable complemented subspaces spanned by subsequences of the natural S…