Essentially Incomparable Banach Spaces of Continuous Functions

Volume 58 / 2010

Rogério Augusto dos Santos Fajardo Bulletin Polish Acad. Sci. Math. 58 (2010), 247-258 MSC: Primary 46E15; Secondary 46B03, 46B20. DOI: 10.4064/ba58-3-7


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 $2^{(2^\omega )}$.


  • Rogério Augusto dos Santos FajardoEscola de Artes, Ciências e Humanidades
    Universidade de São Paulo
    Rua Arlindo Bettio, 1000
    São Paulo, SP, Brazil

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