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Vladikavkaz. Mat. Zh., 2007, Volume 9, Number 1, Pages 16–29 (Mi vmj84)  

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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Bibliographic databases:
UDC: 517.98
MSC: 46A40, 47A65
Received: 15.03.2006

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
\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

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    This publication is cited in the following articles:
    1. A. G. Kusraev, “When all separately band preserving bilinear operators are symmetric?”, Vladikavk. matem. zhurn., 9:2 (2007), 22–25  mathnet  mathscinet
    2. Bu Q., Buskes G., Kusraev A.G., “Bilinear maps on products of vector lattices: A survey”, Positivity, Trends Math., Birkhäuser, Basel, 2007, 97–126  crossref  mathscinet  zmath  isi
    3. A. G. Kusraev, “Hölder type inequalities for orthosymmetric bilinear operators”, Vladikavk. matem. zhurn., 9:3 (2007), 36–46  mathnet  mathscinet
    4. A. G. Kusraev, “An almost $f$-algebra multiplication extends from a majorizing sublattice”, Vladikavk. matem. zhurn., 10:2 (2008), 30–31  mathnet  mathscinet
    5. A. G. Kusraev, “On some properties of orthosymmetric bilinear operators”, Vladikavk. matem. zhurn., 10:3 (2008), 29–33  mathnet  mathscinet
    6. A. E. Gutman, A. G. Kusraev, S. S. Kutateladze, “The Wickstead Problem”, Sib. elektron. matem. izv., 5 (2008), 293–333  mathnet  mathscinet
    7. Kusraev A.G., “A Radon-Nikodým theorem for orthosymmetric bilinear operators”, Positivity, 14:2 (2010), 225–238  crossref  mathscinet  zmath  isi  elib  scopus
    8. Toumi A., Toumi M.A., “Order bounded derivations on Archimedean almost f-algebras”, Positivity, 14:2 (2010), 239–245  crossref  mathscinet  zmath  isi  elib  scopus
    9. Ben Amor F., “On orthosymmetric bilinear maps”, Positivity, 14:1 (2010), 123–134  crossref  mathscinet  zmath  isi  scopus
    10. Kusraev A.G., “A transfer principle for inequalities in vector lattices”, Journal of Mathematical Analysis and Applications, 374:1 (2011), 282–289  crossref  mathscinet  zmath  isi  scopus
    11. Z. A. Kusraeva, “Representation of orthogonally additive polynomials”, Siberian Math. J., 52:2 (2011), 248–255  mathnet  crossref  mathscinet  isi
    12. B. B. Tasoev, “Magaramovo rasshirenie polozhitelnogo ortosimmetrichnogo bilineinogo operatora”, Vladikavk. matem. zhurn., 13:3 (2011), 64–69  mathnet
    13. Z. A. Kusraeva, “Ob odnovremennom prodolzhenii regulyarnykh odnorodnykh ortogonalno additivnykh polinomov”, Vladikavk. matem. zhurn., 13:4 (2011), 28–34  mathnet
    14. Chil E., “Order bounded orthosymmetric bilinear operator”, Czechoslovak Math. J., 61:4 (2011), 873–880  crossref  mathscinet  zmath  isi  scopus
    15. A. G. Kusraev, “Kantorovich's principle in action: $AW^*$-modules and injective Banach lattices”, Vladikavk. matem. zhurn., 14:1 (2012), 67–74  mathnet
    16. Toumi M.A., “Characterization of hyper-Archimedean vector lattices via disjointness preserving bilinear maps”, Algebra Universalis, 67:1 (2012), 29–42  crossref  mathscinet  zmath  isi  scopus
    17. 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  crossref  mathscinet  zmath  isi  scopus
    18. Z. A. Kusraeva, B. B. Tasoev, “O polinomakh Magaram”, Vladikavk. matem. zhurn., 14:4 (2012), 45–51  mathnet
    19. 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  mathnet
    20. Toumi M.A., “A Decomposition of Orthogonally Additive Polynomials on Archimedean Vector Lattices”, Bull. Belg. Math. Soc.-Simon Steven, 20:4 (2013), 621–638  mathscinet  zmath  isi
    21. A. G. Kusraev, S. S. Kutateladze, “On order bounded disjointness preserving operators”, Siberian Math. J., 55:5 (2014), 915–928  mathnet  crossref  mathscinet  isi
    22. Yilmaz R., “the Arens Triadjoints of Some Bilinear Maps”, Filomat, 28:5 (2014), 963–979  crossref  mathscinet  isi  scopus
    23. Toumi M.A., “Orthogonality of Polynomials and Orthosymmetry”, Forum Math., 27:3 (2015), 1389–1400  crossref  mathscinet  zmath  isi  scopus
    24. Z. A. Kusraeva, “Kharakterizatsiya i multiplikativnoe predstavlenie odnorodnykh polinomov, sokhranyayuschikh diz'yunktnost”, Vladikavk. matem. zhurn., 18:1 (2016), 51–62  mathnet
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