Year 2020, Volume 49 , Issue 3, Pages 998 - 1005 2020-06-02

Multiplicative order convergence in $f$-algebras

Abdullah AYDIN [1]


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.
$mo$-convergence, $f$-algebra, $mo$-KB-space, vector lattice
  • [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.
Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0002-0769-5752
Author: Abdullah AYDIN (Primary Author)
Institution: MUŞ ALPARSLAN ÜNİVERSİTESİ
Country: Turkey


Dates

Publication Date : June 2, 2020

Bibtex @research article { hujms512073, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {998 - 1005}, doi = {10.15672/hujms.512073}, title = {Multiplicative order convergence in \$f\$-algebras}, key = {cite}, author = {Aydın, Abdullah} }
APA Aydın, A . (2020). Multiplicative order convergence in $f$-algebras . Hacettepe Journal of Mathematics and Statistics , 49 (3) , 998-1005 . DOI: 10.15672/hujms.512073
MLA Aydın, A . "Multiplicative order convergence in $f$-algebras" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 998-1005 <https://dergipark.org.tr/en/pub/hujms/issue/54699/512073>
Chicago Aydın, A . "Multiplicative order convergence in $f$-algebras". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 998-1005
RIS TY - JOUR T1 - Multiplicative order convergence in $f$-algebras AU - Abdullah Aydın Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.512073 DO - 10.15672/hujms.512073 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 998 EP - 1005 VL - 49 IS - 3 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.512073 UR - https://doi.org/10.15672/hujms.512073 Y2 - 2019 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Multiplicative order convergence in $f$-algebras %A Abdullah Aydın %T Multiplicative order convergence in $f$-algebras %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 3 %R doi: 10.15672/hujms.512073 %U 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
AMA Aydın A . Multiplicative order convergence in $f$-algebras. Hacettepe Journal of Mathematics and Statistics. 2020; 49(3): 998-1005.
Vancouver Aydın A . Multiplicative order convergence in $f$-algebras. Hacettepe Journal of Mathematics and Statistics. 2020; 49(3): 998-1005.