Quotient Banach Lattices Under Unbounded Norm Topology
In this paper, we verify some extra properties in quotient Banach lattices. Especially, we characterize the zero neighborhoods under unbounded norm topology (un-topology) in quotient Banach lattices. We verify some types of convergence in a quotient Banach lattice. Also, we show that if a Banach la...
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| Format: | Article |
| Language: | English |
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University of Maragheh
2024-07-01
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| Series: | Sahand Communications in Mathematical Analysis |
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| Online Access: | https://scma.maragheh.ac.ir/article_714120_6451b1e9264afdb9a0ae7a8633a02076.pdf |
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| _version_ | 1823859370029481984 |
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| author | Leila Hasanzadeh Asghar Ranjbari |
| author_facet | Leila Hasanzadeh Asghar Ranjbari |
| author_sort | Leila Hasanzadeh |
| collection | DOAJ |
| description | In this paper, we verify some extra properties in quotient Banach lattices. Especially, we characterize the zero neighborhoods under unbounded norm topology (un-topology) in quotient Banach lattices. We verify some types of convergence in a quotient Banach lattice. Also, we show that if a Banach lattice is atomic, then the quotient Banach lattice so is. Finally, we show that the quotient preserves Schur and Banach-Saks properties. |
| format | Article |
| id | doaj-art-01361320ed644c888db5389d21201093 |
| institution | Kabale University |
| issn | 2322-5807 2423-3900 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj-art-01361320ed644c888db5389d212010932025-02-11T05:27:31ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002024-07-0121336137010.22130/scma.2024.2022857.1617714120Quotient Banach Lattices Under Unbounded Norm TopologyLeila Hasanzadeh0Asghar Ranjbari1Department of Pure Mathematics, Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, Tabriz, Iran.Department of Pure Mathematics, Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, Tabriz, Iran.In this paper, we verify some extra properties in quotient Banach lattices. Especially, we characterize the zero neighborhoods under unbounded norm topology (un-topology) in quotient Banach lattices. We verify some types of convergence in a quotient Banach lattice. Also, we show that if a Banach lattice is atomic, then the quotient Banach lattice so is. Finally, we show that the quotient preserves Schur and Banach-Saks properties.https://scma.maragheh.ac.ir/article_714120_6451b1e9264afdb9a0ae7a8633a02076.pdfquotient banach latticeun-topologyatom |
| spellingShingle | Leila Hasanzadeh Asghar Ranjbari Quotient Banach Lattices Under Unbounded Norm Topology Sahand Communications in Mathematical Analysis quotient banach lattice un-topology atom |
| title | Quotient Banach Lattices Under Unbounded Norm Topology |
| title_full | Quotient Banach Lattices Under Unbounded Norm Topology |
| title_fullStr | Quotient Banach Lattices Under Unbounded Norm Topology |
| title_full_unstemmed | Quotient Banach Lattices Under Unbounded Norm Topology |
| title_short | Quotient Banach Lattices Under Unbounded Norm Topology |
| title_sort | quotient banach lattices under unbounded norm topology |
| topic | quotient banach lattice un-topology atom |
| url | https://scma.maragheh.ac.ir/article_714120_6451b1e9264afdb9a0ae7a8633a02076.pdf |
| work_keys_str_mv | AT leilahasanzadeh quotientbanachlatticesunderunboundednormtopology AT asgharranjbari quotientbanachlatticesunderunboundednormtopology |