Abstract
We prove that each bounded orthogonally additive homogeneous polynomial acting from an Archimedean vector lattice into a separated convex bornological space, under the additional assumption that the bornological space is complete or the vector lattice is uniformly complete, can be represented as the composite of a bounded linear operator and a special homogeneous polynomial which plays the role of the exponentiation absent in the vector lattice. The approach suggested is based on the notions of convex bornology and vector lattice power.
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