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

Volume 168 / 2005

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


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.


  • Piotr KoszmiderDepartamento de Matemática
    Universidade de São Paulo
    Caixa Postal 66281
    São Paulo, SP
    CEP: 05315-970, Brasil

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