On the Structure of the Spreading Models of a Banach Space Academic Article uri icon

abstract

  • We study some questions concerning the structure of the set of spreading models of a separable infinite-dimensional Banach space X. In particular we give an example of a reflexive X so that all spreading models of X contain ℓ1 but none of them is isomorphic to ℓ1. We also prove that for any countable set C of spreading models generated by weakly null sequences there is a spreading model generated by a weakly null sequence which dominates each element of C. In certain cases this ensures that X admits, for each α < ω1, a spreading model (x̃ i(α))i such that if α < β then (x̃i(α))i; is dominated by (and not equivalent to) (x̃i(β))i. Some applications of these ideas are used to give sufficient conditions on a Banach space for the existence of a subspace and an operator defined on the subspace, which is not a compact perturbation of a multiple of the inclusion map. © Canadian Mathematical Society 2005.

author list (cited authors)

  • Androulakis, G., Odell, E., Schlumprecht, T. h., & Tomczak-Jaegermann, N.

citation count

  • 18

publication date

  • August 2005