Representation of orthogonally additive polynomials |
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Authors: | Z A Kusraeva |
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Institution: | (1) Department of Mathematics, Wesleyan University, Middletown, CT 06457, USA;(2) 5 W. Oak St., Ramsey, NJ 07446, USA |
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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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Keywords: | |
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