International Journal of Nonlinear Analysis and Applications
On a topology induced by order convergence of monotone nets
Document Type : Research Paper
Authors
1 Department of Mathematics, Sarab Branch, Islamic Azad University, Sarab, Iran
2 Department of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran
Abstract
In this paper, we will study on some topologies induced by order convergence in a Riesz space. We will investigate the relationships of them.
Keywords
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50, American Mathematical Society, Providence, RI, 2002.
[2] C.D. Aliprantis and O. Burkinshaw, Positive operators, Springer, Berlin, 2006.
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[5] R. DeMarr, Order convergence in linear topological spaces, Pac. J. Math. 14 (1964), 17–20.[6] R. Demarr, Partially ordered linear spaces and locally convex linear topological spaces, Illinois J. Math. 8 (1964),
601–606.
[7] Y. Deng, M. O’Brien and VG. Troitsky, Unbounded norm convergence in Banach lattices, Positivity 21 (2017),
no. 3, 963–974.
[8] M. Matin, K. Haghnejad Azar and R. Alavizadeh, Weakly Unbounded Norm Topology and wun-Dunford-Pettis
Operators, arXiv preprint (2020) arXiv:2006.05857.
[9] W. Rudin, Functional analysis, Third Ed. McGraw-Hill. Inc., New York, 1991. (Bachelor thesis), Universiteit
Leiden, 2012.
[10] B.Z. Vulikh and O.S. Korsakova, Spaces in which convergence in norm coincides with order convergence, Mat.
Zametki 13 (1973), 259–268.
[11] O. Zabeti, Unbounded absolute weak convergence in Banach lattices, Positivity 22 (2018), no. 2, 501–505.
50, American Mathematical Society, Providence, RI, 2002.
[2] C.D. Aliprantis and O. Burkinshaw, Positive operators, Springer, Berlin, 2006.
[3] I.I. Chuchaev, Ordered locally convex spaces in which the topological and order convergence coincide, Sibirsk Mat.
Zh. 17 (1976), 1395–1402.
[4] Y.A. Dabboorasad, E.Y. Emelyanov and M.A.A. Marabeh, Order convergence is not topological in infinitedimensional vector lattices, Uzbek Math. J. 1 (2020), 159–166.
[5] R. DeMarr, Order convergence in linear topological spaces, Pac. J. Math. 14 (1964), 17–20.[6] R. Demarr, Partially ordered linear spaces and locally convex linear topological spaces, Illinois J. Math. 8 (1964),
601–606.
[7] Y. Deng, M. O’Brien and VG. Troitsky, Unbounded norm convergence in Banach lattices, Positivity 21 (2017),
no. 3, 963–974.
[8] M. Matin, K. Haghnejad Azar and R. Alavizadeh, Weakly Unbounded Norm Topology and wun-Dunford-Pettis
Operators, arXiv preprint (2020) arXiv:2006.05857.
[9] W. Rudin, Functional analysis, Third Ed. McGraw-Hill. Inc., New York, 1991. (Bachelor thesis), Universiteit
Leiden, 2012.
[10] B.Z. Vulikh and O.S. Korsakova, Spaces in which convergence in norm coincides with order convergence, Mat.
Zametki 13 (1973), 259–268.
[11] O. Zabeti, Unbounded absolute weak convergence in Banach lattices, Positivity 22 (2018), no. 2, 501–505.
)
Volume 13, Issue 2
July 2022Pages 1319-1324
- Receive Date: 27 August 2021
- Revise Date: 03 December 2021
- Accept Date: 15 December 2021