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

Piotr Koszmider. "A space C(K) where all nontrivial complemented subspaces have big densities." Studia Mathematica 168.2 (2005): 109-127. <http://eudml.org/doc/284976>.

@article{PiotrKoszmider2005,
abstract = {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.},
author = {Piotr Koszmider},
journal = {Studia Mathematica},
keywords = {Banach space; forcing; density},
language = {eng},
number = {2},
pages = {109-127},
title = {A space C(K) where all nontrivial complemented subspaces have big densities},
url = {http://eudml.org/doc/284976},
volume = {168},
year = {2005},
}

TY - JOUR
AU - Piotr Koszmider
TI - A space C(K) where all nontrivial complemented subspaces have big densities
JO - Studia Mathematica
PY - 2005
VL - 168
IS - 2
SP - 109
EP - 127
AB - 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.
LA - eng
KW - Banach space; forcing; density
UR - http://eudml.org/doc/284976
ER -