On large indecomposable Banach spaces
Functional Analysis
2012-01-18 v2 General Topology
Logic
Operator Algebras
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).
Cite
@article{arxiv.1106.2916,
title = {On large indecomposable Banach spaces},
author = {Piotr Koszmider},
journal= {arXiv preprint arXiv:1106.2916},
year = {2012}
}