Sobczyk's theorems from A to B.

Cabello Sánchez, Félix, Fernández Castillo, Jesús M., and Yost, David. "Sobczyk's theorems from A to B.." Extracta Mathematicae 15.2 (2000): 391-420. <http://eudml.org/doc/38637>.

@article{CabelloSánchez2000,
abstract = {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∞.},
author = {Cabello Sánchez, Félix, Fernández Castillo, Jesús M., Yost, David},
journal = {Extracta Mathematicae},
keywords = {Espacios de Banach; Subespacios K complementados; Espacios normados; Sobczyk's theorems; Phillips's theorem},
language = {eng},
number = {2},
pages = {391-420},
title = {Sobczyk's theorems from A to B.},
url = {http://eudml.org/doc/38637},
volume = {15},
year = {2000},
}

TY - JOUR
AU - Cabello Sánchez, Félix
AU - Fernández Castillo, Jesús M.
AU - Yost, David
TI - Sobczyk's theorems from A to B.
JO - Extracta Mathematicae
PY - 2000
VL - 15
IS - 2
SP - 391
EP - 420
AB - 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∞.
LA - eng
KW - Espacios de Banach; Subespacios K complementados; Espacios normados; Sobczyk's theorems; Phillips's theorem
UR - http://eudml.org/doc/38637
ER -