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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm91-2-2,
author = {Walden Freedman},
title = {An extension property for Banach spaces},
journal = {Colloquium Mathematicae},
volume = {91},
year = {2002},
pages = {167-182},
zbl = {1028.46020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm91-2-2}
}
Walden Freedman. An extension property for Banach spaces. Colloquium Mathematicae, Tome 91 (2002) pp. 167-182. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm91-2-2/