The classification of injective Banach lattices |
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Authors: | P. J. Mangheni |
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Affiliation: | (1) Department of Mathematics, Makerere University, P.O. Box 7062, Kampala, Uganda |
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Abstract: | LetE be a 1-injective Banach lattice,X any Banach space andT: E ← X a norm bounded linear operator. Then eitherT is an isomorphism on some copy ofl ∞ inE or for all σ > 0 there is φ ∈E + ′ such that ‖Tu‖≦φ (|u|)+σ ‖u‖ for allu ∈E. We deduce the theorem that: A norm order continuous injective Banach lattice is order isomorphic to an (AL)-space. |
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