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• W129641750 abstract "This chapter describes the duality in ordered Banach spaces. The real Banach spaces that are partially ordered by means of a closed convex cone are discussed. The principal source of examples for ordered Banach spaces consists of the A ( K ) spaces. The ordering is the natural one, induced by taking P as the cone of non-negative functions. The cone P in A ( K ) has the additional feature of having a nonempty interior. It is shown that a linear space with an appropriately defined order unit can be made into a (normed) order unit space. This provides a strictly order-theoretic characterization of A ( K ) spaces. It is assumed that u is an Archimedean order unit for ( E, P ). It is found that p is a norm on E with unit ball I in which E is a normed order unit space with order unit u and closed convex positive cone P ." @default.
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• W129641750 date "1980-01-01" @default.
• W129641750 modified "2023-09-26" @default.
• W129641750 title "Duality in Ordered Banach Spaces" @default.
• W129641750 doi "https://doi.org/10.1016/b978-0-12-065340-9.50007-3" @default.
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