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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 {\displaystyle } whose norm satisfies ‖ sup { x , y } ‖ = sup { ‖ x ‖ , ‖ y ‖ } {\displaystyle \left\|\sup\{x,y\}\right\|=\sup \left\{\|x\|,\|y\|\right\}} 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 := { 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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