Abstract
A monomial in finite collection of homogeneous polynomials is a point-wise product of these polynomials each raised to some power. It was established in [14] and [15] that, given a finite set of positive linear operators acting from an Archimedean vector lattice into an f-algebra with multiplicative unit, the corresponding monomial is orthogonally additive polynomial if and only if the collection of these operators is a disjointness preserving set. It is shown in this paper that a similar result is also true in the case when the target space is a uniformly complete vector lattice. Moreover, the result remains valid if we replace the linear operators with homogeneous orthogonally additive polynomials. The correct definition of monomials in homogeneous polynomials is guaranteed by the homogeneous functional calculus and the concavification procedure.
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The research of Zalina A. Kusraeva was executed at the Regional Mathematical Center of Southern Federal University with the support of the Ministry of Science and Higher Education of the Russian Federation, agreement No 075-02-2023-924.
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The research was executed at the Regional mathematical center of Southern Federal University with the support of the Ministry of Science and Higher Education of the Russian Federation, agreement No 075-02-2023-924.
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Kusraeva, Z.A., Tamaeva, V.A. ORTHOGONAL ADDITIVITY OF MONOMIALS IN POSITIVE HOMOGENEOUS POLYNOMIALS. J Math Sci 280, 224–233 (2024). https://doi.org/10.1007/s10958-023-06826-y
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DOI: https://doi.org/10.1007/s10958-023-06826-y