Abstract
We show that ifX is a Banach lattice containing no copy ofc 0 and ifZ is a subspace ofX isomorphic toL 1[0, 1] then (a)Z contains a subspaceZ 0 isomorphic toL 1 and complemented inX and (b)X contains a complemented sublattice isomorphic and lattice-isomorphic toL 1.
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References
L. Dor,On projections in L 1, Ann. Math.102 (1975), 463–474.
P. Enflo and T. Starbird,Subspaces of L 1 isomorphic to L1, to appear in Studia Math.
W. B. Johnson, B. Maurey, G. Schechtman and L. Tzafriri,Symmetric structures in Banach spaces, to appear.
N. J. Kalton,The endomorphisms of L p, 0≦p≦1, Indiana Univ. Math. J.27 (1978), 353–381.
H. P. Lotz,The Radon-Nikodym property in Banach lattices, to appear.
H. P. Lotz and H. P. Rosenthal, to appear.
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Kalton, N.J. EmbeddingL 1 in a Banach lattice. Israel J. Math. 32, 209–220 (1979). https://doi.org/10.1007/BF02764917
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DOI: https://doi.org/10.1007/BF02764917