On the Structure of the Spreading Models of a Banach Space

[摘要] We study some questions concerning the structure of theset of spreading models of a separable infinite-dimensional Banachspace $X$. In particular we give an example of a reflexive $X$ so thatall spreading models of $X$ contain $ell_1$ but none of them isisomorphic to $ell_1$. We also prove that for any countable set $C$of spreading models generated by weakly null sequences there is aspreading model generated by a weakly null sequence which dominateseach element of $C$. In certain cases this ensures that $X$ admits,for each $alpha < omega_1$, a spreading model $(ildex_i^{(alpha)})_i$ such that if $alpha < eta$ then $(ildex_i^{(alpha)})_i$ is dominated by (and not equivalent to)$(ilde x_i^{(eta)})_i$. Some applications of these ideas are used togive sufficient conditions on a Banach space for the existence of asubspace and an operator defined on the subspace, which is not acompact perturbation of a multiple of the inclusion map.

[学科分类] 数学（综合）