We study some geometrical properties of a new structure introduced by G. Pisier: the structure of lattice subspaces. We show first that if X and Y are Banach lattices such that , then X is an AL-space or Y is an AM-space. We introduce the notion of homogeneous lattice subspace and we show that up to regular isomorphism, the only homogeneous lattice subspace of , for 2≤ p < ∞, is G(I). We also show a version of the Dvoretzky theorem for this structure. We end this paper by giving an estimate of the regular Banach-Mazur distance between some finite-dimensional lattice subspaces.
@book{bwmeta1.element.bwnjournal-article-doi-10_4064-dm397-0-1,
author = {Jos\'e L. Marcolino Nhani},
title = {La structure des sous-espaces de treillis},
series = {GDML\_Books},
year = {2001},
zbl = {0990.46007},
language = {fra},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-dm397-0-1}
}
José L. Marcolino Nhani. La structure des sous-espaces de treillis. GDML_Books (2001), http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-dm397-0-1/