Abstract
Publisher Summary Most classical Banach spaces are Banach lattices. Compared to the enormous generality of (even separable) Banach spaces, the order structure constitutes a considerable enrichment in both geometric and operator theoretic terms. (For the elementary results of Banach lattice theory needed in the sequel, the reader is referred to either of those monographs.) If E,F denote (real) Banach lattices, a (bounded, linear) operator T : EF is called positive (T > 0) if Tx > 0 for all x > 0 in E; T is called order bounded (or regular) if T is the difference of positive operators.
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