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An almost orthosymmetric bilinear map

Year 2019, Volume: 68 Issue: 2, 2143 - 2153, 01.08.2019
https://doi.org/10.31801/cfsuasmas.515703

Abstract

In this paper, as a generalization of the concept of pseudo-almost f-algebra, we define a new concept of almost orthosymmetric bilinear map on a vector lattice and prove that the Arens triadjoint of a positive almost orthosymmetric bilinear map is positive almost orthosymmetric.This also extends results on the order bidual of pseudo-almost f-algebras.


References

  • Aliprantis, C. D. and Burkinshaw, O., Positive Operators, Academic Press, 1985.
  • Arens, R., Operations induced in function classes, Monatsh. Math., 55, (1951), 1-19.
  • Arens, R., The adjoint of a bilinear operation, Proc. Amer. Math. Soc., 2, (1951), 839-848.
  • Bernau, S. J. and Huijsmans, C. B., The order bidual of almost f-algebras and d-algebras, Trans. Amer. Math. Soc., 347, (1995), 4259-4275.
  • Birkhoff, G. and Pierce, R. S., Lattice-ordered rings, An. Acad. Brasil. Ciénc., 28, (1956), 41-49.
  • Birkhoff, G., Lattice Theory, Amer. Math. Soc. Colloq. Publ. 25, 1967.
  • Boulabiar, K., Buskes G. and Pace, R., Some properties of bilinear maps of order bounded variation, Positivity, 9, (2005), 401-414.
  • Kusraev, A. G., Representation and extension of orthoregular bilinear operators, Vladikavkaz Mat. Zh., 9, (2007), 16-29.
  • Buskes, G. and van Rooij, A., Almost f-algebras: commutativity and Cauchy-Schwarz inequality, Positivity, 4, (2000), 227-231.
  • Buskes, G., Page, R. Jr. and Yilmaz, R., A note on bi-orthomorphisms, Operator Theory: Advances and Applications, 201, (2009), 99-107.
  • Grobler, J. J., Commutativity of Arens product in lattice ordered algebras, Positivity, 3, (1999), 357-364.
  • Kudláček, V., On some types of ℓ-rings, Sborni Vysokého Učeni Techn v Brně, 1-2, (1962), 179-181.
  • Luxemburg, W. A. J. and Zaanen, A. C., Riesz Spaces I, North-Holland, 1971.
  • Yilmaz, R., A Note on bilinear maps on vector lattices, New Trends in Mathematical Sciences, 5 (3), (2017), 168-174.
  • Yılmaz, R.,The Arens triadjoints of some bilinear maps, Filomat, 28 (5), (2014), 963-979.
  • Yilmaz, R., Notes on lattice ordered algebras, Serdica Math. J., 40, (2014), 319-328.
  • Yilmaz, R., The bidual of r-algebras, Ukrainian Mathematical Journal, 63 (5), (2011), 833-837.
  • Zaanen, A. C., Introduction to Operator Theory in Riesz Spaces, Springer, 1997.
Year 2019, Volume: 68 Issue: 2, 2143 - 2153, 01.08.2019
https://doi.org/10.31801/cfsuasmas.515703

Abstract

References

  • Aliprantis, C. D. and Burkinshaw, O., Positive Operators, Academic Press, 1985.
  • Arens, R., Operations induced in function classes, Monatsh. Math., 55, (1951), 1-19.
  • Arens, R., The adjoint of a bilinear operation, Proc. Amer. Math. Soc., 2, (1951), 839-848.
  • Bernau, S. J. and Huijsmans, C. B., The order bidual of almost f-algebras and d-algebras, Trans. Amer. Math. Soc., 347, (1995), 4259-4275.
  • Birkhoff, G. and Pierce, R. S., Lattice-ordered rings, An. Acad. Brasil. Ciénc., 28, (1956), 41-49.
  • Birkhoff, G., Lattice Theory, Amer. Math. Soc. Colloq. Publ. 25, 1967.
  • Boulabiar, K., Buskes G. and Pace, R., Some properties of bilinear maps of order bounded variation, Positivity, 9, (2005), 401-414.
  • Kusraev, A. G., Representation and extension of orthoregular bilinear operators, Vladikavkaz Mat. Zh., 9, (2007), 16-29.
  • Buskes, G. and van Rooij, A., Almost f-algebras: commutativity and Cauchy-Schwarz inequality, Positivity, 4, (2000), 227-231.
  • Buskes, G., Page, R. Jr. and Yilmaz, R., A note on bi-orthomorphisms, Operator Theory: Advances and Applications, 201, (2009), 99-107.
  • Grobler, J. J., Commutativity of Arens product in lattice ordered algebras, Positivity, 3, (1999), 357-364.
  • Kudláček, V., On some types of ℓ-rings, Sborni Vysokého Učeni Techn v Brně, 1-2, (1962), 179-181.
  • Luxemburg, W. A. J. and Zaanen, A. C., Riesz Spaces I, North-Holland, 1971.
  • Yilmaz, R., A Note on bilinear maps on vector lattices, New Trends in Mathematical Sciences, 5 (3), (2017), 168-174.
  • Yılmaz, R.,The Arens triadjoints of some bilinear maps, Filomat, 28 (5), (2014), 963-979.
  • Yilmaz, R., Notes on lattice ordered algebras, Serdica Math. J., 40, (2014), 319-328.
  • Yilmaz, R., The bidual of r-algebras, Ukrainian Mathematical Journal, 63 (5), (2011), 833-837.
  • Zaanen, A. C., Introduction to Operator Theory in Riesz Spaces, Springer, 1997.
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Review Articles
Authors

Ruşen Yılmaz 0000-0003-1579-2234

Publication Date August 1, 2019
Submission Date January 21, 2019
Acceptance Date June 21, 2019
Published in Issue Year 2019 Volume: 68 Issue: 2

Cite

APA Yılmaz, R. (2019). An almost orthosymmetric bilinear map. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 2143-2153. https://doi.org/10.31801/cfsuasmas.515703
AMA Yılmaz R. An almost orthosymmetric bilinear map. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):2143-2153. doi:10.31801/cfsuasmas.515703
Chicago Yılmaz, Ruşen. “An Almost Orthosymmetric Bilinear Map”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 2143-53. https://doi.org/10.31801/cfsuasmas.515703.
EndNote Yılmaz R (August 1, 2019) An almost orthosymmetric bilinear map. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 2143–2153.
IEEE R. Yılmaz, “An almost orthosymmetric bilinear map”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 2143–2153, 2019, doi: 10.31801/cfsuasmas.515703.
ISNAD Yılmaz, Ruşen. “An Almost Orthosymmetric Bilinear Map”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 2143-2153. https://doi.org/10.31801/cfsuasmas.515703.
JAMA Yılmaz R. An almost orthosymmetric bilinear map. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:2143–2153.
MLA Yılmaz, Ruşen. “An Almost Orthosymmetric Bilinear Map”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 2143-5, doi:10.31801/cfsuasmas.515703.
Vancouver Yılmaz R. An almost orthosymmetric bilinear map. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):2143-5.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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