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EmbeddingL 1 in a Banach lattice

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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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Author notes

  1. N. J. Kalton

    Present address: Department of Pure Mathematics, University College of Swansea, Singleton Park, SA2 8PP, Swansea, Wales, U.K.

Authors and Affiliations

  1. Department of Mathematics, University of Illinois, 61801, Urbana, Illinois, USA

    N. J. Kalton

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  1. N. J. Kalton
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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

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