L p ( G , X * ) comme sous-espace complémenté de L q ( G , X ) *

Mohammad Daher

Colloquium Mathematicae (2013)

  • Volume: 131, Issue: 2, page 273-286
  • ISSN: 0010-1354

Abstract

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Let G be a compact metric infinite abelian group and let X be a Banach space. We study the following question: if the dual X* of X does not have the Radon-Nikodym property, is L p ( G , X * ) complemented in L q ( G , X ) * , 1 < p ≤ ∞, 1/p + 1/q = 1, or, if p = 1, in the subspace of C(G,X)* consisting of the measures that are absolutely continuous with respect to the Haar measure? We show that the answer is negative if X is separable and does not contain ℓ¹, and if 1 ≤ p < ∞. If p = 1, this answers a question of G. Emmanuele. We show that the answer is positive if X* is a Banach lattice that does not contain a copy of c₀, 1 ≤ p < ∞. It is also positive, by a different method, if p = ∞ and X* = M(K), where K is a compact space with a perfect subset. Moreover, we examine whether C Λ ( G , X * ) may be complemented in L Λ ∞ ( G , X * ) , where Λ is a subset of Γ, the dual group of G, when the space X is separable and L ¹ ( G , X ) / L ¹ Λ c ( G , X ) does not contain ℓ¹.

How to cite

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Mohammad Daher. "$L^{p}(G,X*)$ comme sous-espace complémenté de $L^{q}(G,X)*$." Colloquium Mathematicae 131.2 (2013): 273-286. <http://eudml.org/doc/286271>.

@article{MohammadDaher2013,
author = {Mohammad Daher},
journal = {Colloquium Mathematicae},
language = {fre},
number = {2},
pages = {273-286},
title = {$L^\{p\}(G,X*)$ comme sous-espace complémenté de $L^\{q\}(G,X)*$},
url = {http://eudml.org/doc/286271},
volume = {131},
year = {2013},
}

TY - JOUR
AU - Mohammad Daher
TI - $L^{p}(G,X*)$ comme sous-espace complémenté de $L^{q}(G,X)*$
JO - Colloquium Mathematicae
PY - 2013
VL - 131
IS - 2
SP - 273
EP - 286
LA - fre
UR - http://eudml.org/doc/286271
ER -

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