On the structure of the spreading models of a Banach space
| dc.creator | Androulakis, G. | |
| dc.creator | Odell, E. | |
| dc.creator | Schlumprecht, Th. | |
| dc.creator | Tomczak-Jaegermann, N. | |
| dc.date | 2003-05-05 | |
| dc.date.accessioned | 2026-07-07T04:57:47Z | |
| dc.date.available | 2026-07-07T04:57:47Z | |
| dc.description | 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 $\ell_1$ but none of them is isomorphic to $\ell_1$. 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 $α< ω_1$, a spreading model $(\tilde x_i^α)_i$ such that if $α< β$ then $(\tilde x_i^α)_i$ is dominated by (and not equivalent to) $(\tilde x_i^β)_i$. 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. | |
| dc.identifier | https://arxiv.org/abs/math/0305082 | |
| dc.identifier | http://arxiv.org/abs/math/0305082 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67379 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46B03; 47A05 | |
| dc.title | On the structure of the spreading models of a Banach space | |
| dc.type | text |