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Order bounded orthosymmetric bilinear operator

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Abstract

It is proved by an order theoretical and purely algebraic method that any order bounded orthosymmetric bilinear operator b: E×E → F where E and F are Archimedean vector lattices is symmetric. This leads to a new and short proof of the commutativity of Archimedean almost f-algebras.

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References

  1. C.D. Aliprantis, O. Burkinshaw: Positive Operators. Springer, Berlin, 2006.

    MATH  Google Scholar 

  2. M. Basly, A. Triki: FF-algèbres Archimédiennes réticulées. University of Tunis, Preprint, 1988.

    Google Scholar 

  3. S. J. Bernau, C.B. Huijsmans: Almost f-algebras and d-algebras. Math. Proc. Camb. Philos. Soc. 107 (1990), 287–308.

    Article  MathSciNet  MATH  Google Scholar 

  4. A. Bigard, K. Keimel, S. Wolfenstein: Groupes et Anneaux Réticulés. Lecture Notes in Mathematics Vol. 608. Springer, Berlin-Heidelberg-New York, 1977.

    MATH  Google Scholar 

  5. G. Birkhoff, R. S. Pierce: Lattice-ordered rings. Anais Acad. Brasil. Ci. 28 (1956), 41–69.

    MathSciNet  Google Scholar 

  6. Q. Bu, G. Buskes, A.G. Kusraev: Bilinear Maps on Product of Vector Lattices: A Survey. Positivity. Trends in Mathematics. Birkhäuser, Basel, 2007, pp. 97–126.

    Google Scholar 

  7. G. Buskes, B. de Pagter, A. van Rooij: Functional calculus in Riesz spaces. Indag. Math. New Ser. 4 (1991), 423–436.

    Article  Google Scholar 

  8. G. Buskes, A.G. Kusraev: Representation and extension of orthoregular bilinear operators. Vladikavkaz. Math. Zh. 9 (2007), 16–29.

    MathSciNet  Google Scholar 

  9. G. Buskes, A. van Rooij: Small Riesz spaces. Math. Proc. Camb. Philos. Soc. 105 (1989), 523–536.

    Article  MATH  Google Scholar 

  10. G. Buskes, A. van Rooij: Almost f-algebras: Commutativity and the Cauchy-Schwarz inequality. Positivity 4 (2000), 227–231.

    Article  MathSciNet  MATH  Google Scholar 

  11. G. Buskes, A. van Rooij: Squares of Riesz spaces. Rocky Mt. J. Math. 31 (2001), 45–56.

    Article  MATH  Google Scholar 

  12. G. Buskes, A. van Rooij: Bounded variation and tensor products of Banach lattices. Positivity 7 (2003), 47–59.

    Article  MathSciNet  MATH  Google Scholar 

  13. J. J. Grobler, C.C.A. Labuschagne: The tensor product of Archimedean ordered vector spaces. Math. Proc. Camb. Philos. Soc. 104 (1988), 331–345.

    Article  MathSciNet  MATH  Google Scholar 

  14. C.B. Huijsmans, B. de Pagter: Subalgebras and Riesz subspaces of an f-algebra. Proc. Lond. Math. Soc. III. Ser. 48 (1984), 161–174.

    Article  MATH  Google Scholar 

  15. W.A. J. Luxemburg, A.C. Zaanen: Riesz spaces I. North-HollandMathematical Library, Amsterdam-London, 1971.

  16. H. Nakano: Product spaces of semi-ordered linear spaces. J. Fac. Sci., Hakkaidô Univ. Ser. I. 12 (1953), 163–210.

    MATH  Google Scholar 

  17. A.C. Zaanen: Riesz spaces II. North-Holland Mathematical Library, Amsterdam-New York-Oxford, 1983.

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  1. Institut préparatoire aux études d’ingenieurs de Tunis, 2 Rue Jawaher Lel Nehrou, 1008, Montfleury, Tunisia

    Elmiloud Chil

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  1. Elmiloud Chil
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Correspondence to Elmiloud Chil.

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Chil, E. Order bounded orthosymmetric bilinear operator. Czech Math J 61, 873–880 (2011). https://doi.org/10.1007/s10587-011-0052-8

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  • DOI: https://doi.org/10.1007/s10587-011-0052-8

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