It follows from our earlier results [Israel J. Math., to appear] that in the Gurariy space G every finite-dimensional smooth subspace is contained in a bigger smooth subspace. We show that this property does not characterise the Gurariy space among Lindenstrauss spaces and we provide various examples to show that C(K) spaces do not have this property.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm222-2-3,
author = {V. P. Fonf and P. Wojtaszczyk},
title = {Extension of smooth subspaces in Lindenstrauss spaces},
journal = {Studia Mathematica},
volume = {223},
year = {2014},
pages = {157-163},
zbl = {1311.46012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm222-2-3}
}
V. P. Fonf; P. Wojtaszczyk. Extension of smooth subspaces in Lindenstrauss spaces. Studia Mathematica, Tome 223 (2014) pp. 157-163. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm222-2-3/