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- W2051642098 abstract "Let E be a Banach lattice and E 0 an ideal of E . Let f be a positive norm-bounded order continuous functional on E 0 . Then f has a norm preserving positive order continuous extension to E . Moreover, there exists a minimum extension among all such extensions. This result enables us to obtain an isometric lattice homomorphism from ( E 0 ) ∗ n into E ∗ n . As an application, we prove that if F is a Banach lattice and if E 0 is the ideal generated by F in E (= F ∗∗ ), then ( E 0 ) ∗ n can be identified with F ∗ in the canonical sense. Certain extension properties of order continuous functionals thus follow. Banach lattices with strictly monotone norm are also investigated." @default.
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- W2051642098 date "1994-01-01" @default.
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- W2051642098 title "Extension properties of order continuous functionals and applications to the theory of Banach lattices" @default.
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- W2051642098 doi "https://doi.org/10.1016/0019-3577(94)90037-x" @default.
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