Essentially Incomparable Banach Spaces of Continuous Functions

Rogério Augusto dos Santos Fajardo. "Essentially Incomparable Banach Spaces of Continuous Functions." Bulletin of the Polish Academy of Sciences. Mathematics 58.3 (2010): 247-258. <http://eudml.org/doc/281158>.

@article{RogérioAugustodosSantosFajardo2010,
abstract = {We construct, under Axiom ♢, a family $(C(K_ξ))_\{ξ<2^\{(2^ω)\}\}$ of indecomposable Banach spaces with few operators such that every operator from $C(K_ξ)$ into $C(K_η)$ 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 $2^ω$ instead of $2^\{(2^ω)\}$.},
author = {Rogério Augusto dos Santos Fajardo},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {diamond axiom; indecomposable Banach spaces; few operators; incomparable},
language = {eng},
number = {3},
pages = {247-258},
title = {Essentially Incomparable Banach Spaces of Continuous Functions},
url = {http://eudml.org/doc/281158},
volume = {58},
year = {2010},
}

TY - JOUR
AU - Rogério Augusto dos Santos Fajardo
TI - Essentially Incomparable Banach Spaces of Continuous Functions
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2010
VL - 58
IS - 3
SP - 247
EP - 258
AB - We construct, under Axiom ♢, a family $(C(K_ξ))_{ξ<2^{(2^ω)}}$ of indecomposable Banach spaces with few operators such that every operator from $C(K_ξ)$ into $C(K_η)$ 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 $2^ω$ instead of $2^{(2^ω)}$.
LA - eng
KW - diamond axiom; indecomposable Banach spaces; few operators; incomparable
UR - http://eudml.org/doc/281158
ER -