Geodesic
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 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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

Rogério Augusto dos Santos Fajardo 1

1 Escola de Artes, Ciências e Humanidades Universidade de São Paulo Rua Arlindo Bettio, 1000 São Paulo, SP, Brazil 
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     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
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Rogério Augusto dos Santos Fajardo. Essentially Incomparable Banach Spaces of
 Continuous Functions. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 58 (2010) no. 3, pp. 247-258. doi: 10.4064/ba58-3-7

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