A Note on bilinear maps on vector lattices

A Note on bilinear maps on vector lattices

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  • C. D. Aliprantis and O. Burkinshaw, Positive Operators, Academic Press, 1985.
  • R. Arens, The adjoint of a bilinear operation, Proc. Amer. Math. Soc. 2 (1951), 839-848.
  • S. J. Bernau and C. B. Huijsmans, The order bidual of almost f -algebras and d-algebras, Trans. Amer. Math. Soc. 347 (1995), 4259-4275.
  • G. Birkhoff and R. S. Pierce, Lattice-ordered rings, An. Acad. Brasil. Cienc. 28 (1956), 41-49.
  • G. Birkhoff, Lattice Theory, Amer. Math. Soc. Colloq. Publ. No. 25 (1967).
  • K. Boulabiar and W. Brahmi, Multiplicative structure of biorthomorphisms and embedding of orthomorphisms, Indagationes Mathematicae 27 (2016), 786-798.
  • K. Boulabiar, G. Buskes and R. Pace, Some properties of bilinear maps of order bounded variation, Positivity 9 (2005), 401-414.
  • A. G. Kusraev, Representation and extension of orthoregular bilinear operators, Vladikavkaz Mat. Zh. 9 (2007), 16-29.
  • G. Buskes and A. van Rooij, Squares of Riesz spaces, Rocky Mountain J. Math.31 (2001), 45-56.
  • G. Buskes and A. van Rooij, Almost f -algebras: commutativity and Cauchy-Schwarz inequality, Positivity 4 (2000), 227-231.
  • G. Buskes, R. Page Jr and R. Yilmaz, A note on bi-orthomorphisms, Vector Measures, Integration and Related Topics, Operator Theory: Advances and Applications, Vol. 201 (2009), 99-107.
  • V. Kudlacek, On some types of ℓ-rings, Sborni Vysokeho Uceni Techn v Brne 1-2 (1962), 179-181.
  • W. A. J. Luxemburg and A. C. Zaanen, Riesz Spaces I, North-Holland, 1971.
  • M. A. Toumi, The triadjoint of an orthosymmetric bimorphism, Czechoslovak Mathematical Journal, 60 (135) (2010), 85-94.
  • R. Yilmaz and K. Rowlands, On orthomorphisms, quasi-orthomorphisms and quasi-multipliers, J. Math. Anal. Appl. 313 (2006), 120-131.
  • R. Yılmaz, The Arens triadjoints of some bilinear maps, Filomat 28:5 (2014), 963-979.
  • A. C. Zaanen, Introduction to Operator Theory in Riesz Spaces, Springer, 1997.