There is no bound on sizes of indecomposable Banach spaces

  title={There is no bound on sizes of indecomposable Banach spaces},
  author={Piotr Koszmider and Saharon Shelah and Michal 'Swicetek},
  journal={arXiv: Functional Analysis},
Assuming the generalized continuum hypothesis we construct arbitrarily big indecomposable Banach spaces. i.e., such that whenever they are decomposed as $X\oplus Y$, then one of the closed subspaces $X$ or $Y$ must be finite dimensional. It requires alternative techniques compared to those which were initiated by Gowers and Maurey or Argyros with the coauthors. This is because hereditarily indecomposable Banach spaces always embed into $\ell_\infty$ and so their density and cardinality is… Expand
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