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A hereditarily indecomposable $ {\mathcal{L}_{\infty}} $ -space that solves the scalar-plus-compact problem

Spiros A. Argyros Department of Mathematics, National Technical University of Athens Richard G. Haydon Brasenose College, Oxford, U.K.

TBD mathscidoc:1701.332023

Acta Mathematica, 206, (1), 1-54, 2009.3
We construct a hereditarily indecomposable Banach space with dual space isomorphic to$ℓ$_{1}. Every bounded linear operator on this space is expressible as λ$I$+$K$, with λ a scalar and$K$compact.
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@inproceedings{spiros2009a,
  title={A hereditarily indecomposable $ {\mathcal{L}_{\infty}} $ -space that solves the scalar-plus-compact problem},
  author={Spiros A. Argyros, and Richard G. Haydon},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203355940117734},
  booktitle={Acta Mathematica},
  volume={206},
  number={1},
  pages={1-54},
  year={2009},
}
Spiros A. Argyros, and Richard G. Haydon. A hereditarily indecomposable $ {\mathcal{L}_{\infty}} $ -space that solves the scalar-plus-compact problem. 2009. Vol. 206. In Acta Mathematica. pp.1-54. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203355940117734.
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