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An almost orthosymmetric bilinear map

Year 2019, , 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, , 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

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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