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

• Autorzy: Piotr Koszmider
• Języki publikacji: EN

Abstrakty

EN

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 κ 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.

Kategorie tematyczne

• 46B03: Isomorphic theory (including renorming) of Banach spaces
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 168
• Numer: 2
• Strony: 109-127

Daty

wydano

2005

Twórcy

autor

Piotr Koszmider

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

Identyfikatory

DOI

10.4064/sm168-2-2