There is no bound on sizes of indecomposable Banach spaces

The obtained Banach spaces are of the form C(K) for some compact connected Hausdorff space and have few operators in the sense that every linear bounded operator T on C(K) for every f∈C(K) satisfies T(f)=gf+S(f) where g∈C(K) and S is weakly compact or equivalently strictly singular. In particular, the spaces carry the structure of a Banach algebra and in the complex case even the structure of a C⁎-algebra.