[Banach] Abstract of a paper by S.A. Argyros, V. Kanellopoulos, and K. Tyros

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