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Operators on Banach lattices as weighted compositions. (English) Zbl 0564.46016

Lattice homomorphisms and disjointness preserving operators between Banach lattices having locally compact representation spaces are studied. These operators are described as weighted composition operators with respect to the representation spaces. Specifically, \(Tf=rf\circ \phi\) for r a scale valued function and \(\phi\) a map between representation spaces. These results then permit an analysis of the principal order ideal generated by a homomorphism.

MSC:

46B42 Banach lattices
47B60 Linear operators on ordered spaces
47B38 Linear operators on function spaces (general)
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