Dual Banach spaces which contain an isometric copy of L₁

2000/04/27 by S. J. Dilworth, Dilworth, S. J., Maria Girardi +3
Mathematics · #46B04 (primary) #46B20 (secondary) #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46B04 #msc:46B20

paper · pdf · doi:10.48550/arxiv.math/0004168

12 pages

arxiv created 2000/04/27 · arxiv updated 2009/11/30

Abstract

A Banach space contains asymptotically isometric copies of ℓ₁ if and only if its dual space contains an isometric copy of L₁.

Related

• A note on asymptotically isometric copies of l¹ and c₀
• On Banach spaces whose duals are isomorphic to l₁
• A Banach subspace of L_1/2 which does not embed in L₁ (isometric version)
• (1+)-complemented, (1+)-isomorphic copies of L₁ in dual Banach spaces
• The dual of a non-reflexive L-embedded Banach space contains ℓ^∞ isometrically.