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Essentially incomparable Banach spaces of continuous functions

Fajardo R. A.

Bulletin of the Polish Academy of Sciences. Mathematics

2010

Vol. 58, no 3

247-258

We construct, under Axiom 0, a family (C(Kξ))ξ < 2(2ω) of indecomposable Banach spaces with few operators such that every operator from C(Kξ) into C(Kη) is weakly compact, for all ξ ≠ η. In particular, these spaces are pairwise essentially incomparable. Assuming no additional set-theoretic axiom, we obtain this result with size 2ω instead of 2(2ω).