La structure des sous-espaces de treillis

José L. Marcolino Nhani

  • 2001

Abstract

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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.

How to cite

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José L. Marcolino Nhani. La structure des sous-espaces de treillis. 2001. <http://eudml.org/doc/285989>.

@book{JoséL2001,
author = {José L. Marcolino Nhani},
keywords = {Banach lattice; cross norm; Dvoretzky theorem; Gaussian space; homogeneous Banach lattice; lattice subspace structure; Rademacher subspace; regular operator; regular Banach-Mazur distance; property (P); injective tensor norm; regular isomorphism; regular isometry; Rademacher functions; AM-spaces},
language = {fre},
title = {La structure des sous-espaces de treillis},
url = {http://eudml.org/doc/285989},
year = {2001},
}

TY - BOOK
AU - José L. Marcolino Nhani
TI - La structure des sous-espaces de treillis
PY - 2001
LA - fre
KW - Banach lattice; cross norm; Dvoretzky theorem; Gaussian space; homogeneous Banach lattice; lattice subspace structure; Rademacher subspace; regular operator; regular Banach-Mazur distance; property (P); injective tensor norm; regular isomorphism; regular isometry; Rademacher functions; AM-spaces
UR - http://eudml.org/doc/285989
ER -

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