This is an announcement for the paper "The stabilized set of $p$'s in Krivine's theorem can be disconnected" by Kevin Beanland, Daniel Freeman and Pavlos Motakis.

Abstract: For any closed subset $F$ of $[1,\infty]$ which is either finite or consists of the elements of an increasing sequence and its limit, a reflexive Banach space $X$ with a 1-unconditional basis is constructed so that in each block subspace $Y$ of $X$, $\ell_p$ is finitely block represented in $Y$ if and only if $p \in F$. In particular, this solves the question as to whether the stabilized Krivine set for a Banach space had to be connected. We also prove that for every infinite dimensional subspace $Y$ of $X$ there is a dense subset $G$ of $F$ such that the spreading models admitted by $Y$ are exactly the $\ell_p$ for $p\in G$.

Archive classification: math.FA

Mathematics Subject Classification: 46B03, 46B06, 46B07, 46B25, 46B45

Remarks: 25 pages

Submitted from: pmotakis@central.ntua.gr

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

http://front.math.ucdavis.edu/1408.0265

or

http://arXiv.org/abs/1408.0265