On large indecomposable Banach spaces

Details On large indecomposable Banach spaces On large indecomposable Banach spaces

2011-06-15

arxiv.org/abs/1106.2916v2

Mathematics

Functional Analysis

Scientific paper

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).

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