This is an announcement for the paper "Spreading models in Banach space theory" by S.A. Argyros, V. Kanellopoulos, and K. Tyros.

Abstract: 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.

Archive classification: math.FA math.CO

Remarks: vi+115 pages

Submitted from: ktyros@central.ntua.gr

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1006.0957

or

http://arXiv.org/abs/1006.0957