Geodesic
Homogeneous Orthogonally Additive Polynomials on Vector Lattices
Matematičeskie zametki, Tome 91 (2012) no. 5, pp. 704-710

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It is proved that an orthogonally additive order bounded homogeneous polynomial acting between uniformly complete vector lattices admits a representation in the form of the composition of a linear order bounded operator and a special homogeneous polynomial playing the role of a power-law function, which is absent in the vector lattice. This result helps to establish a criterion for the integral representability of an orthogonally additive homogeneous polynomial.
Keywords: vector lattice, relatively uniform convergence, linear order bounded operator, orthogonally additive order bounded homogeneous polynomial. 
@article{MZM_2012_91_5_a5,
     author = {Z. A. Kusraeva},
     title = {Homogeneous {Orthogonally} {Additive} {Polynomials} on {Vector} {Lattices}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {704--710},
     publisher = {mathdoc},
     volume = {91},
     number = {5},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_5_a5/}
}
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Z. A. Kusraeva. Homogeneous Orthogonally Additive Polynomials on Vector Lattices. Matematičeskie zametki, Tome 91 (2012) no. 5, pp. 704-710. http://geodesic.mathdoc.fr/item/MZM_2012_91_5_a5/