On Antichains of Spreading Models of Banach Spaces
نویسنده
چکیده
We show that for every separable Banach space X, either SPw(X) (the set of all spreading models of X generated by weakly-null sequences in X, modulo equivalence) is countable, or SPw(X) contains an antichain of the size of the continuum. This answers a question of S. J. Dilworth, E. Odell and B. Sari.
منابع مشابه
Uniform Homeomorphisms of Banach Spaces and Asymptotic Structure
We give a general result on the behavior of spreading models in Banach spaces which coarse Lipschitz-embed into asymptotically uniformly convex spaces. We use this result to study the uniqueness of the uniform structure in p-sums of finite-dimensional spaces for 1 < p < ∞; in particular we give some new examples of spaces with unique uniform structure.
متن کاملLattice Structures and Spreading Models
We consider problems concerning the partial order structure of the set of spreading models of Banach spaces. We construct examples of spaces showing that the possible structure of these sets include certain classes of finite semi-lattices and countable lattices and all finite lattices.
متن کاملOn Asymptotic Models in Banach Spaces
A well known application of Ramsey’s Theorem to Banach Space Theory is the notion of a spreading model (ẽi) of a normalized basic sequence (xi) in a Banach space X. We show how to generalize the construction to define a new creature (ei), which we call an asymptotic model of X. Every spreading model of X is an asymptotic model of X and in most settings, such as if X is reflexive, every normaliz...
متن کاملStrictly Singular Non-compact Operators on Hereditarily Indecomposable Banach Spaces
An example is given of a strictly singular non-compact operator on a Hereditarily Indecomposable, reflexive, asymptotic `1 Banach space. The construction of this operator relies on the existence of transfinite c0-spreading models in the dual of the space.
متن کاملar X iv : m at h . FA / 0 50 86 50 v 1 3 1 A ug 2 00 5 LATTICE STRUCTURES AND SPREADING MODELS
We consider problems concerning the partial order structure of the set of spreading models of Banach spaces. We construct examples of spaces showing that the possible structure of these sets include certain classes of finite semi-lattices and countable lattices, and all finite lattices.
متن کامل