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Year 2020, Volume: 49 Issue: 3, 998 - 1005, 02.06.2020
https://doi.org/10.15672/hujms.512073

Abstract

References

  • [1] C.D. Aliprantis and O. Burkinshaw, Positive Operators, Springer, Dordrecht, 2006.
  • [2] A. Aydın, Unbounded $p_\tau$ -convergence in vector lattice normed by locally solid lat- tices, Academic Studies in Mathematic and Natural Sciences-2019/2, 118–134, IVPE, Cetinje-Montenegro, 2019.
  • [3] A. Aydın, S.G. Gorokhova and H. Gül, Nonstandard hulls of lattice-normed ordered vector spaces, Turkish J. Math. 42 (1), 155–163, 2018.
  • [4] A. Aydın, E. Emel’yanov, N. Erkurşun-Özcan and M.A.A. Marabeh, Compact-like operators in lattice-normed spaces, Indag. Math. 2 (1), 633–656, 2018.
  • [5] A. Aydin, E. Emel’yanov, N. Erkurşun-Özcan and M.A.A. Marabeh, Unbounded p- convergence in lattice-normed vector lattices, Sib. Adv. Math. 29 (3), 164–182, 2019.
  • [6] N. Gao, V.G. Troitsky and F. Xanthos, Uo-convergence and its applications to Cesáro means in Banach lattices, Isr. J. Math. 220 (2), 649–689, 2017.
  • [7] B.Z. Vulikh, Introduction to the Theory of Partially Ordered Spaces, Wolters- Noordhoff Scientific, Groningen, 1967.
  • [8] A.C. Zaanen, Riesz Spaces II, North-Holland Publishing C., Amsterdam, 1983.

Multiplicative order convergence in $f$-algebras

Year 2020, Volume: 49 Issue: 3, 998 - 1005, 02.06.2020
https://doi.org/10.15672/hujms.512073

Abstract

A net $(x_\alpha)$ in an $f$-algebra $E$ is said to be multiplicative order convergent to $x\in E$ if $\left|x_\alpha-x\right|u\oc 0$ for all $u\in E_+$. In this paper, we introduce the notions $mo$-convergence, $mo$-Cauchy, $mo$-complete, $mo$-continuous, and $mo$-KB-space. Moreover, we study the basic properties of these notions.

References

  • [1] C.D. Aliprantis and O. Burkinshaw, Positive Operators, Springer, Dordrecht, 2006.
  • [2] A. Aydın, Unbounded $p_\tau$ -convergence in vector lattice normed by locally solid lat- tices, Academic Studies in Mathematic and Natural Sciences-2019/2, 118–134, IVPE, Cetinje-Montenegro, 2019.
  • [3] A. Aydın, S.G. Gorokhova and H. Gül, Nonstandard hulls of lattice-normed ordered vector spaces, Turkish J. Math. 42 (1), 155–163, 2018.
  • [4] A. Aydın, E. Emel’yanov, N. Erkurşun-Özcan and M.A.A. Marabeh, Compact-like operators in lattice-normed spaces, Indag. Math. 2 (1), 633–656, 2018.
  • [5] A. Aydin, E. Emel’yanov, N. Erkurşun-Özcan and M.A.A. Marabeh, Unbounded p- convergence in lattice-normed vector lattices, Sib. Adv. Math. 29 (3), 164–182, 2019.
  • [6] N. Gao, V.G. Troitsky and F. Xanthos, Uo-convergence and its applications to Cesáro means in Banach lattices, Isr. J. Math. 220 (2), 649–689, 2017.
  • [7] B.Z. Vulikh, Introduction to the Theory of Partially Ordered Spaces, Wolters- Noordhoff Scientific, Groningen, 1967.
  • [8] A.C. Zaanen, Riesz Spaces II, North-Holland Publishing C., Amsterdam, 1983.
There are 8 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Abdullah Aydın 0000-0002-0769-5752

Publication Date June 2, 2020
Published in Issue Year 2020 Volume: 49 Issue: 3

Cite

APA Aydın, A. (2020). Multiplicative order convergence in $f$-algebras. Hacettepe Journal of Mathematics and Statistics, 49(3), 998-1005. https://doi.org/10.15672/hujms.512073
AMA Aydın A. Multiplicative order convergence in $f$-algebras. Hacettepe Journal of Mathematics and Statistics. June 2020;49(3):998-1005. doi:10.15672/hujms.512073
Chicago Aydın, Abdullah. “Multiplicative Order Convergence in $f$-Algebras”. Hacettepe Journal of Mathematics and Statistics 49, no. 3 (June 2020): 998-1005. https://doi.org/10.15672/hujms.512073.
EndNote Aydın A (June 1, 2020) Multiplicative order convergence in $f$-algebras. Hacettepe Journal of Mathematics and Statistics 49 3 998–1005.
IEEE A. Aydın, “Multiplicative order convergence in $f$-algebras”, Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 3, pp. 998–1005, 2020, doi: 10.15672/hujms.512073.
ISNAD Aydın, Abdullah. “Multiplicative Order Convergence in $f$-Algebras”. Hacettepe Journal of Mathematics and Statistics 49/3 (June 2020), 998-1005. https://doi.org/10.15672/hujms.512073.
JAMA Aydın A. Multiplicative order convergence in $f$-algebras. Hacettepe Journal of Mathematics and Statistics. 2020;49:998–1005.
MLA Aydın, Abdullah. “Multiplicative Order Convergence in $f$-Algebras”. Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 3, 2020, pp. 998-1005, doi:10.15672/hujms.512073.
Vancouver Aydın A. Multiplicative order convergence in $f$-algebras. Hacettepe Journal of Mathematics and Statistics. 2020;49(3):998-1005.