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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Original Russian Text Copyright © 2011 Kusraeva Z. A.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 52, No. 2, pp. 315–325, March–April, 2011.
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Kusraeva, Z.A. Representation of orthogonally additive polynomials. Sib Math J 52, 248–255 (2011). https://doi.org/10.1134/S003744661102008X
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DOI: https://doi.org/10.1134/S003744661102008X