Spreading Models in Banach Space Theory

Details Spreading Models in Banach Space Theory Spreading Models in Banach Space Theory

2010-06-04

arxiv.org/abs/1006.0957v1

Mathematics

Functional Analysis

vi+115 pages

Scientific paper

We extend the classical Brunel-Sucheston definition of the spreading model by introducing the $\mathcal{F}$-sequences $(x_s)_{s\in\mathcal{F}}$ in a Banach space and the plegma families in $\mathcal{F}$ where $\mathcal{F}$ is a regular thin family. The new concept yields a transfinite increasing hierarchy of classes of 1-subsymmetric sequences. We explore the corresponding theory and we present examples establishing this hierarchy and illustrating the limitation of the theory.

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