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arXiv · 1105.2732

Finite order spreading models

S. A. Argyros·V. Kanellopoulos·K. Tyros
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Abstract

Extending the classical notion of the spreading model, the $k$-spreading models of a Banach space are introduced, for every $k\in\mathbb{N}$. The definition, which is based on the $k$-sequences and plegma families, reveals a new class of spreading sequences associated to a Banach space. Most of the results of the classical theory are stated and proved in the higher order setting. Moreover, new phenomena like the universality of the class of the 2-spreading models of $c_0$ and the composition property are established. As consequence, a problem concerning the structure of the $k$-iterated spreading models is solved.

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S. A. Argyros, V. Kanellopoulos, K. Tyros. 2011-05-13. Finite order spreading models. https://arxiv.org/abs/1105.2732

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