An extension property for Banach spaces

Walden Freedman. "An extension property for Banach spaces." Colloquium Mathematicae 91.2 (2002): 167-182. <http://eudml.org/doc/284091>.

@article{WaldenFreedman2002,
abstract = {A Banach space X has property (E) if every operator from X into c₀ extends to an operator from X** into c₀; X has property (L) if whenever K ⊆ X is limited in X**, then K is limited in X; X has property (G) if whenever K ⊆ X is Grothendieck in X**, then K is Grothendieck in X. In all of these, we consider X as canonically embedded in X**. We study these properties in connection with other geometric properties, such as the Phillips properties, the Gelfand-Phillips and weak Gelfand-Phillips properties, and the property of being a Grothendieck space.},
author = {Walden Freedman},
journal = {Colloquium Mathematicae},
keywords = {weak Phillips property; property (V*); Grothendieck spaces; Sobczyk's Theorem; extension property; lifting property},
language = {eng},
number = {2},
pages = {167-182},
title = {An extension property for Banach spaces},
url = {http://eudml.org/doc/284091},
volume = {91},
year = {2002},
}

TY - JOUR
AU - Walden Freedman
TI - An extension property for Banach spaces
JO - Colloquium Mathematicae
PY - 2002
VL - 91
IS - 2
SP - 167
EP - 182
AB - A Banach space X has property (E) if every operator from X into c₀ extends to an operator from X** into c₀; X has property (L) if whenever K ⊆ X is limited in X**, then K is limited in X; X has property (G) if whenever K ⊆ X is Grothendieck in X**, then K is Grothendieck in X. In all of these, we consider X as canonically embedded in X**. We study these properties in connection with other geometric properties, such as the Phillips properties, the Gelfand-Phillips and weak Gelfand-Phillips properties, and the property of being a Grothendieck space.
LA - eng
KW - weak Phillips property; property (V*); Grothendieck spaces; Sobczyk's Theorem; extension property; lifting property
UR - http://eudml.org/doc/284091
ER -