This is an announcement for the paper "A $c_0$ saturated Banach space with tight structure" by Spiros A. Argyros and Giorgos Petsoulas.
Abstract: It is shown that variants of the HI methods could yield objects closely connected to the classical Banach spaces. Thus we present a new $c_0$ saturated space, denoted as $\mathfrak{X}_0$, with rather tight structure. The space $\mathfrak{X}_0$ is not embedded into a space with an unconditional basis and its complemented subspaces have the following structure. Everyone is either of type I, namely, contains an isomorph of $\mathfrak{X}_0$ itself or else is isomorphic to a subspace of $c_0$ (type II). Furthermore for any analytic decomposition of $\mathfrak{X}_0$ into two subspaces one is of type I and the other is of type II. The operators of $\mathfrak{X}_0$ share common features with those of HI spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B26
Remarks: 24 pages
Submitted from: sargyros@math.ntua.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1012.2758
or