Essentially Incomparable Banach Spaces of Continuous Functions
Volume 58 / 2010
Bulletin Polish Acad. Sci. Math. 58 (2010), 247-258
MSC: Primary 46E15; Secondary 46B03, 46B20.
DOI: 10.4064/ba58-3-7
Abstract
We construct, under Axiom $\diamondsuit $, a family $(C(K_\xi ))_{\xi <2^{(2^\omega )}}$ of indecomposable Banach spaces with few operators such that every operator from $C(K_\xi )$ into $C(K_\eta )$ is weakly compact, for all $\xi \not =\eta $. In particular, these spaces are pairwise essentially incomparable.
Assuming no additional set-theoretic axiom, we obtain this result with size $2^\omega $ instead of $2^{(2^\omega )}$.
