This is an announcement for the paper "Higher order spreading models" by S. A. Argyros, V. Kanellopoulos, and K. Tyros.

Abstract: We introduce the higher order spreading models associated to a Banach space $X$. Their definition is based on $\ff$-sequences $(x_s)_{s\in\ff}$ with $\ff$ a regular thin family and the plegma families. We show that the higher order spreading models of a Banach space $X$ form an increasing transfinite hierarchy $(\mathcal{SM}_\xi(X))_{\xi<\omega_1}$. Each $\mathcal{SM}_\xi (X)$ contains all spreading models generated by $\ff$-sequences $(x_s)_{s\in\ff}$ with order of $\ff$ equal to $\xi$. We also provide a study of the fundamental properties of the hierarchy.

Archive classification: math.FA

Mathematics Subject Classification: Primary 46B03, 46B06, 46B25, 46B45, Secondary 05D10

Remarks: 37 pages

Submitted from: chcost@gmail.com

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

http://front.math.ucdavis.edu/1202.6390

or

http://arXiv.org/abs/1202.6390