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This article is cited in 23 scientific papers (total in 24 papers)
Representation and extension of orthoregular bilinear operators
G. Buskesa, A. G. Kusraevb
a Department of Mathematics, University of Mississippi, USA
b Institute of Applied Mathematics and Informatics,
Vladikavkaz Science Center of the RAS,
Vladikavkaz, Russia
Abstract:
In this paper we study some important structural properties of orthosymmetric bilinear operators using the concept of the square of an Archimedean vector lattice. Some new results on extension and analytical representation of such operators are presented.
Key words:
vector lattice, positive bilinear operator, orthosymmetric bilinear operator, orthoregular bilinear operator, lattice bimorphism.
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UDC:
517.98
MSC: 46A40, 47A65
Received: 15.03.2006
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Citation:
G. Buskes, A. G. Kusraev, “Representation and extension of orthoregular bilinear operators”, Vladikavkaz. Mat. Zh., 9:1 (2007), 16–29
Citation in format AMSBIB
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\by G.~Buskes, A.~G.~Kusraev
\paper Representation and extension of orthoregular bilinear operators
\jour Vladikavkaz. Mat. Zh.
\yr 2007
\vol 9
\issue 1
\pages 16--29
\mathnet{http://mi.mathnet.ru/vmj84}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2434620}
\elib{http://elibrary.ru/item.asp?id=11620326}
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Russian articles,
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This publication is cited in the following articles:
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A. G. Kusraev, “When all separately band preserving bilinear operators are symmetric?”, Vladikavk. matem. zhurn., 9:2 (2007), 22–25
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Bu Q., Buskes G., Kusraev A.G., “Bilinear maps on products of vector lattices: A survey”, Positivity, Trends Math., Birkhäuser, Basel, 2007, 97–126
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A. G. Kusraev, “Hölder type inequalities for orthosymmetric bilinear operators”, Vladikavk. matem. zhurn., 9:3 (2007), 36–46
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A. G. Kusraev, “An almost $f$-algebra multiplication extends from a majorizing sublattice”, Vladikavk. matem. zhurn., 10:2 (2008), 30–31
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A. G. Kusraev, “On some properties of orthosymmetric bilinear operators”, Vladikavk. matem. zhurn., 10:3 (2008), 29–33
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A. E. Gutman, A. G. Kusraev, S. S. Kutateladze, “The Wickstead Problem”, Sib. elektron. matem. izv., 5 (2008), 293–333
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Kusraev A.G., “A Radon-Nikodým theorem for orthosymmetric bilinear operators”, Positivity, 14:2 (2010), 225–238
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Toumi A., Toumi M.A., “Order bounded derivations on Archimedean almost f-algebras”, Positivity, 14:2 (2010), 239–245
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Ben Amor F., “On orthosymmetric bilinear maps”, Positivity, 14:1 (2010), 123–134
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Kusraev A.G., “A transfer principle for inequalities in vector lattices”, Journal of Mathematical Analysis and Applications, 374:1 (2011), 282–289
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Z. A. Kusraeva, “Representation of orthogonally additive polynomials”, Siberian Math. J., 52:2 (2011), 248–255
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B. B. Tasoev, “Magaramovo rasshirenie polozhitelnogo ortosimmetrichnogo bilineinogo operatora”, Vladikavk. matem. zhurn., 13:3 (2011), 64–69
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Z. A. Kusraeva, “Ob odnovremennom prodolzhenii regulyarnykh odnorodnykh ortogonalno additivnykh polinomov”, Vladikavk. matem. zhurn., 13:4 (2011), 28–34
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Chil E., “Order bounded orthosymmetric bilinear operator”, Czechoslovak Math. J., 61:4 (2011), 873–880
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A. G. Kusraev, “Kantorovich's principle in action: $AW^*$-modules and injective Banach lattices”, Vladikavk. matem. zhurn., 14:1 (2012), 67–74
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Toumi M.A., “Characterization of hyper-Archimedean vector lattices via disjointness preserving bilinear maps”, Algebra Universalis, 67:1 (2012), 29–42
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Ibort A., Linares P., Llavona J.G., “A representation theorem for orthogonally additive polynomials on Riesz spaces”, Rev. Mat. Complut., 25:1 (2012), 21–30
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Z. A. Kusraeva, B. B. Tasoev, “O polinomakh Magaram”, Vladikavk. matem. zhurn., 14:4 (2012), 45–51
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S. K. Vodopyanov, E. I. Gordon, A. E. Gutman, A. V. Koptev, S. S. Kutateladze, S. A. Malyugin, Yu. G. Reshetnyak, “Anatoliyu Georgievichu Kusraevu — 60 let”, Sib. elektron. matem. izv., 10 (2013), 13–29
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Toumi M.A., “A Decomposition of Orthogonally Additive Polynomials on Archimedean Vector Lattices”, Bull. Belg. Math. Soc.-Simon Steven, 20:4 (2013), 621–638
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A. G. Kusraev, S. S. Kutateladze, “On order bounded disjointness preserving operators”, Siberian Math. J., 55:5 (2014), 915–928
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Yilmaz R., “the Arens Triadjoints of Some Bilinear Maps”, Filomat, 28:5 (2014), 963–979
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Toumi M.A., “Orthogonality of Polynomials and Orthosymmetry”, Forum Math., 27:3 (2015), 1389–1400
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Z. A. Kusraeva, “Kharakterizatsiya i multiplikativnoe predstavlenie odnorodnykh polinomov, sokhranyayuschikh diz'yunktnost”, Vladikavk. matem. zhurn., 18:1 (2016), 51–62
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