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Sibirsk. Mat. Zh., 2011, Volume 52, Number 2, Pages 315–325 (Mi smj2199)  

This article is cited in 9 scientific papers (total in 9 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.

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English version:
Siberian Mathematical Journal, 2011, 52:2, 248–255

Bibliographic databases:

UDC: 517.98
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

Citation in format AMSBIB
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\by Z.~A.~Kusraeva
\paper Representation of orthogonally additive polynomials
\jour Sibirsk. Mat. Zh.
\yr 2011
\vol 52
\issue 2
\pages 315--325
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\yr 2011
\vol 52
\issue 2
\pages 248--255
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Z. A. Kusraeva, “Ob odnovremennom prodolzhenii regulyarnykh odnorodnykh ortogonalno additivnykh polinomov”, Vladikavk. matem. zhurn., 13:4 (2011), 28–34  mathnet
    2. Kusraeva Z.A., “Ortosimmetrichnost otnositelno lineinogo operatora”, Matematicheskii forum (Itogi nauki. Yug Rossii), 5 (2011), 135–138  elib
    3. Z. A. Kusraeva, B. B. Tasoev, “O polinomakh Magaram”, Vladikavk. matem. zhurn., 14:4 (2012), 45–51  mathnet
    4. Z. A. Kusraeva, “Odnorodnye polinomy, srednie stepennye i srednie geometricheskie v vektornykh reshetkakh”, Vladikavk. matem. zhurn., 16:4 (2014), 49–53  mathnet
    5. Ben Amor F., “Orthogonally Additive Homogenous Polynomials on Vector Lattices”, Commun. Algebr., 43:3 (2015), 1118–1134  crossref  mathscinet  zmath  isi  scopus
    6. Z. A. Kusraeva, “Kharakterizatsiya i multiplikativnoe predstavlenie odnorodnykh polinomov, sokhranyayuschikh diz'yunktnost”, Vladikavk. matem. zhurn., 18:1 (2016), 51–62  mathnet
    7. A. G. Kusraev, “Domination Problem in Banach Lattices”, Math. Notes, 100:1 (2016), 66–79  mathnet  crossref  crossref  mathscinet  isi  elib
    8. Z. A. Kusraeva, “On compact domination of homogeneous orthogonally additive polynomials”, Siberian Math. J., 57:3 (2016), 519–524  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    9. Kusraeva Z.A., “Powers of Quasi-Banach Lattices and Orthogonally Additive Polynomials”, J. Math. Anal. Appl., 458:1 (2018), 767–780  crossref  mathscinet  zmath  isi  scopus
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