Sobczyk's theorem is usually stated as: every copy of c0 inside a separable Banach space is complemented by a projection with norm at most 2. Nevertheless, our understanding is not complete until we also recall: and c0 is not complemented in l∞ . Now the limits of the phenomenon are set: although c0 is complemented in separable superspaces, it is not necessarily complemented in a non-separable superspace, such as l∞.
@article{urn:eudml:doc:38637,
title = {Sobczyk's theorems from A to B.},
journal = {Extracta Mathematicae},
volume = {15},
year = {2000},
pages = {391-420},
zbl = {0990.46003},
mrnumber = {MR1823898},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38637}
}
Cabello Sánchez, Félix; Fernández Castillo, Jesús M.; Yost, David. Sobczyk's theorems from A to B.. Extracta Mathematicae, Tome 15 (2000) pp. 391-420. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38637/