Israel Journal of Mathematics

, Volume 31, Issue 2, pp 169–179 | Cite as

Embeddings ofC(Δ) andL 1[0, 1] in Banach lattices

  • Heinrich P. Lotz
  • Haskell P. Rosenthal


It is proved that ifE is a separable Banach lattice withE′ weakly sequentially complete,F is a Banach space andT:E→F is a bounded linear operator withT′F′ non-separable, then there is a subspaceG ofE, isomorphic toC(Δ), such thatT G is an isomorphism, whereC(Δ) denotes the space of continuous real valued functions on the Cantor discontinuum. This generalizes an earlier result of the second-named author. A number of conditions are proved equivalent for a Banach latticeE to contain a subspace order isomorphic toC(Δ). Among them are the following:L 1 is lattice isomorphic to a sublattice ofE′;C(Δ)′ is lattice isomorphic to a sublattice ofE′; E contains an order bounded sequence with no weak Cauchy subsequence;E has a separable closed sublatticeF such thatF′ does not have a weak order unit.


Banach Space Banach Lattice Order Interval Compact Hausdorff Space Lattice Homomorphism 
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Copyright information

© Hebrew University 1978

Authors and Affiliations

  • Heinrich P. Lotz
    • 1
  • Haskell P. Rosenthal
    • 1
  1. 1.University of Illinois at Urbana-ChampaignUrbanaUSA

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