ﻻ يوجد ملخص باللغة العربية
If alpha and beta are countable ordinals such that beta eq 0, denote by tilde{T}_{alpha,beta} the completion of $c_{00}$ with respect to the implicitly defined norm ||x|| = max{||x||_{c_{0}}, 1/2 sup sum_{i=1}^{j}||E_{i}x||}, where the supremum is taken over all finite subsets E_{1},...,E_{j} of $mathbb{N}$ such that $E_{1}<...<E_{j}$ and {min E_{1},...,min E_{j}} in S_beta. It is shown that the Bourgain $ell^{1}$-index of tilde{T}_{alpha,beta} is omega^{alpha+beta.omega}. In particular, if alpha =omega^{alpha_{1}}. m_{1}+...+omega^{alpha_{n}}. m_{n} in Cantor normal form and alpha_{n} is not a limit ordinal, then there exists a Banach space whose ell^{1}-index is omega^{alpha}.
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 (theta _n)_{n=1}^{infty} is a nonincreasing null sequence in (0,1). In this paper, we compute the Bourgain ell^1 - in
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 the mixed Tsirelson space X=T[(theta _n,S_n)_{n=1}^{infty}] (1)Every
In this paper, we study minimality properties of partly modified mixed Tsirelson spaces. A Banach space with a normalized basis (e_k) is said to be subsequentially minimal if for every normalized block basis (x_k) of (e_k), there is a further block (
Suppose that (F_n)_{n=1}^{infty} is a sequence of regular families of finite subsets of N and (theta_n)_{n=1}^{infty} is a nonincreasing null sequence in (0,1). The mixed Tsirelson space T[(theta_{n}, F_n)_{n=1}^{infty}] is the completion of $c_{00}$
We investigate an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters. We assume that each cluster is composed of identical units (monomers) and we allow mass to be lost, gained or conserved du