# Sobczyk's theorems from A to B.

Félix Cabello Sánchez; Jesús M. Fernández Castillo; David Yost

Extracta Mathematicae (2000)

- Volume: 15, Issue: 2, page 391-420
- ISSN: 0213-8743

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topCabello 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 -

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