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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
Article

Abstract

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.

Keywords

Banach Space Banach Lattice Order Interval Compact Hausdorff Space Lattice Homomorphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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