1996/10/07 by N. J. Kalton, Nigel J. Kalton, Kalton, Nigel J. +3
Mathematics · #43A46 #46B03 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:43A46 #msc:46B03
paper · pdf · doi:10.48550/arxiv.math/9610211
arxiv created 1996/10/07 · openalex publication_date 1996/10/07 · arxiv updated 2009/11/30 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
If Q is a surjection from L1(μ), μ σ-finite, onto a Banach space containing c0 then (*) ker Q is uncomplemented in its second dual. If Q is a surjection from an \cal L1-space onto a Banach space containing uniformly ℓn^∞ (n=1,2,…) then (**) there exists a bounded linear operator from ker Q into a Hilbert space which is not 2-absolutely summing. Let S be an infinite Sidon set in the dual group Γ of a compact abelian group G. Then L1_S(G)=\f∈ L1(G): f(γ)=0 for γ∈ S\ satisfies (*) and (**) hence L1_S(G) is not an \cal L1-space and is not isomorphic to a Banach lattice.