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Sibirskii Matematicheskii Zhurnal, 2011, Volume 52, Number 2, Pages 315–325
(Mi smj2199)
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This article is cited in 26 scientific papers (total in 26 papers)
Representation of orthogonally additive polynomials
Z. A. Kusraeva South Mathematical Institute of VSC RAS, Vladikavkaz, Russia
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.
Keywords:
vector lattice power, convex bornology, orthogonally additive polynomial, polylinear operator, orthosymmetry.
Received: 06.05.2010
Citation:
Z. A. Kusraeva, “Representation of orthogonally additive polynomials”, Sibirsk. Mat. Zh., 52:2 (2011), 315–325; Siberian Math. J., 52:2 (2011), 248–255
Linking options:
https://www.mathnet.ru/eng/smj2199 https://www.mathnet.ru/eng/smj/v52/i2/p315
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