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A Note on bilinear maps on vector lattices

Year 2017, Volume: 5 Issue: 3, 168 - 174, 01.07.2017

Rusen Yilmaz

Abstract


Keywords

Arens adjoint vector lattice order bidual d-algebra d-bimorphism

References

  • 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.

Year 2017, Volume: 5 Issue: 3, 168 - 174, 01.07.2017

Rusen Yilmaz

Abstract

References

  • 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.
There are 17 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Rusen Yilmaz

Publication Date July 1, 2017
Published in Issue Year 2017 Volume: 5 Issue: 3

Cite

APA Yilmaz, R. (2017). A Note on bilinear maps on vector lattices. New Trends in Mathematical Sciences, 5(3), 168-174.
AMA Yilmaz R. A Note on bilinear maps on vector lattices. New Trends in Mathematical Sciences. July 2017;5(3):168-174.
Chicago Yilmaz, Rusen. “A Note on Bilinear Maps on Vector Lattices”. New Trends in Mathematical Sciences 5, no. 3 (July 2017): 168-74.
EndNote Yilmaz R (July 1, 2017) A Note on bilinear maps on vector lattices. New Trends in Mathematical Sciences 5 3 168–174.
IEEE R. Yilmaz, “A Note on bilinear maps on vector lattices”, New Trends in Mathematical Sciences, vol. 5, no. 3, pp. 168–174, 2017.
ISNAD Yilmaz, Rusen. “A Note on Bilinear Maps on Vector Lattices”. New Trends in Mathematical Sciences 5/3 (July 2017), 168-174.
JAMA Yilmaz R. A Note on bilinear maps on vector lattices. New Trends in Mathematical Sciences. 2017;5:168–174.
MLA Yilmaz, Rusen. “A Note on Bilinear Maps on Vector Lattices”. New Trends in Mathematical Sciences, vol. 5, no. 3, 2017, pp. 168-74.
Vancouver Yilmaz R. A Note on bilinear maps on vector lattices. New Trends in Mathematical Sciences. 2017;5(3):168-74.
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