This is an announcement for the paper "On large indecomposable Banach spaces" by Piotr Koszmider.

Abstract: Hereditarily indecomposable Banach spaces may have density at most continuum (Plichko-Yost, Argyros-Tolias). In this paper we show that this cannot be proved for indecomposable Banach spaces. We provide the first example of an indecomposable Banach space of density two to continuum. The space exists consistently, is of the form C(K) and it has few operators in the sense that any bounded linear operator T on C(K) satisfies T(f)=gf+S(f) for every f in C(K), where g is in C(K) and S is weakly compact (strictly singular).

Archive classification: math.FA math.GN math.LO

Submitted from: piotr.math@gmail.com

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

http://front.math.ucdavis.edu/1106.2916

or

http://arXiv.org/abs/1106.2916