RT Journal Article
T1 On l 1   subspaces of Orlicz vector-valued function spaces.
A1 Bombal Gordón, Fernando
AB The author studies those Orlicz vector-valued function spaces that contain a copy or a complemented copy of l 1  . Precisely, given a finite complete measure space (S,Σ,μ) , a Young function Φ , and a Banach space E , let L Φ (S,Σ,μ,E)  denote the vector space of all (classes of) strongly measurable functions f  from S  to E  such that ∫Φ(k∥f∥)dμ<∞  for some k>0 , and let L Φ (μ)=L Φ (S,Σ,μ,R) . The author first extends a result of G. Pisier concerning vector-valued L p   function spaces by showing that if l 1   embeds in L Φ (S,Σ,μ,E) , then l 1   embeds either in L Φ (μ)  or in E . This result, combined with a result of E. Saab and the reviewer concerning the embedding of l 1   as a complemented subspace of the Banach space of all E -valued continuous functions on a compact Hausdorff space, is used to show that if in addition E  is a Banach lattice, if Φ  satisfies the Δ 2  -condition and if μ  is nonpurely atomic, then L Φ (S,Ω,μ,E)  contains a complemented copy of l 1   if and only if either L Φ (μ)  or E  contains a complemented copy of l 1
PB Cambridge Univ Press
SN 0305-0041
YR 1987
FD 1987
LK https://hdl.handle.net/20.500.14352/64755
UL https://hdl.handle.net/20.500.14352/64755
LA eng
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DS Docta Complutense
RD 3 may 2024