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In mathematics, specifically in order theory and functional analysis, an abstract m-space or an AM-space is a Banach lattice whose norm satisfies for all x and y in the positive cone of X. We say that an AM-space X is an AM-space with unit if in addition there exists some u ≥ 0 in X such that the interval [−u, u] := { z ∈ X : −u ≤ z and z ≤ u } is equal to the unit ball of X; such an element u is unique and an order unit of X.
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