# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## A space $C(K)$ where all nontrivial complemented subspaces have big densities

### Tom 168 / 2005

Studia Mathematica 168 (2005), 109-127 MSC: 03E35, 46B03. DOI: 10.4064/sm168-2-2

#### Streszczenie

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.

#### Autorzy

• Piotr KoszmiderDepartamento de Matemática