Large sublattices in subsets of Banach lattices

Large sublattices in subsets of Banach lattices A classical problem (initially studied by N. Kalton and A. Wilansky) concerns finding closed infinite dimensional subspaces of X / Y, where Y is a subspace of a Banach space X. We study the Banach lattice analogue of this question. For a Banach lattice X, we prove that X / Y contains a closed infinite dimensional sublattice under the following conditions: either (i) Y is a closed infinite codimensional subspace of X, and X is either order continuous or a C(K) space, where K is a compact subset of $${\mathbb {R}}^n$$ R n ; or (ii) Y is the range of a compact operator. Archiv der Mathematik Springer Journals

Large sublattices in subsets of Banach lattices

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Springer International Publishing
Copyright © 2017 by Springer International Publishing AG
Mathematics; Mathematics, general
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