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La structure des sous-espaces de treillis

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Nhani J.

Instytut Matematyczny Polskiej Akademii Nauk

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 $B_{r}(X,Y) = B(X,Y)$, 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 $L^{p}(Ω,μ)$, 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.

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1 Nhani J.

1 2001

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La structure des sous-espaces de treillis