Essentially Incomparable Banach Spaces of Continuous Functions

Rogério Augusto dos Santos Fajardo¹

¹ Escola de Artes, Ciências e Humanidades Universidade de São Paulo Rua Arlindo Bettio, 1000 São Paulo, SP, Brazil

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 58 (2010) no. 3, pp. 247-258.

Résumé

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

Détail

DOI : 10.4064/ba58-3-7

Keywords: construct under axiom diamondsuit family omega indecomposable banach spaces few operators every operator eta weakly compact eta particular these spaces pairwise essentially incomparable assuming additional set theoretic axiom obtain result size omega instead omega