Geodesic
A space $C(K)$ where all nontrivial complemented subspaces have big densities
Piotr Koszmider1
1 Departamento de Matemática Universidade de São Paulo Caixa Postal 66281 São Paulo, SP CEP: 05315-970, Brasil
Studia Mathematica, Tome 168 (2005) no. 2, pp. 109-127

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Using the method of forcing we prove that consistently there is a Banach space (of continuous functions on a totally disconnected compact Hausdorff space) of density $\kappa $ bigger than the continuum where all operators are multiplications by a continuous function plus a weakly compact operator and which has no infinite-dimensional complemented subspaces of density continuum or smaller. In particular no separable infinite-dimensional subspace has a complemented superspace of density continuum or smaller, consistently answering a question of Johnson and Lindenstrauss of 1974.
DOI : 10.4064/sm168-2-2
Keywords: using method forcing prove consistently there banach space continuous functions totally disconnected compact hausdorff space density kappa bigger continuum where operators multiplications continuous function plus weakly compact operator which has infinite dimensional complemented subspaces density continuum smaller particular separable infinite dimensional subspace has complemented superspace density continuum smaller consistently answering question johnson lindenstrauss

Piotr Koszmider 1

1 Departamento de Matemática Universidade de São Paulo Caixa Postal 66281 São Paulo, SP CEP: 05315-970, Brasil 
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Piotr Koszmider. A space $C(K)$ where all nontrivial complemented
  subspaces have big densities. Studia Mathematica, Tome 168 (2005) no. 2, pp. 109-127. doi: 10.4064/sm168-2-2

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