Banach spaces with an unconditional basis that are isomorphic to a nonatomic Banach lattice

McClaran, Lea

doi:10.1090/S0002-9939-1995-1254847-0

Banach spaces with an unconditional basis that are isomorphic to a nonatomic Banach lattice
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Proc. Amer. Math. Soc. 123 (1995), 471-476 Request permission

Abstract:

It is proved that if X is a Banach space with an unconditional basis, then X is isomorphic to a nonatomic Banach lattice which is not order continuous if and only if X contains a subspace isomorphic to ${c_0}$.

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