Uniformly closed sublattices of finite codimension
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914709734686720 |
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| author | Bilokopytov, Eugene Troitsky, Vladimir G. |
| author_facet | Bilokopytov, Eugene Troitsky, Vladimir G. |
| contents | The paper investigates uniformly closed subspaces, sublattices, and ideals of finite codimension in Archimedean vector lattices. It is shown that every uniformly closed subspace (or sublattice) of finite codimension may be written as an intersection of uniformly closed subspaces (respectively, sublattices) of codimension one. Every uniformly closed sublattice of codimension $n$ contains a uniformly closed ideal of codimension at most $2n$. If the vector lattice is uniformly complete then every ideal of finite codimension is uniformly closed. Results of the paper extend (and are motivated by) results of [AL90a,AL90b] and , as well as Kakutani's characterization of closed sublattices of $C(K)$ spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_08805 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Uniformly closed sublattices of finite codimension Bilokopytov, Eugene Troitsky, Vladimir G. Functional Analysis Primary: 46A40. Secondary: 46B42, 46E05 The paper investigates uniformly closed subspaces, sublattices, and ideals of finite codimension in Archimedean vector lattices. It is shown that every uniformly closed subspace (or sublattice) of finite codimension may be written as an intersection of uniformly closed subspaces (respectively, sublattices) of codimension one. Every uniformly closed sublattice of codimension $n$ contains a uniformly closed ideal of codimension at most $2n$. If the vector lattice is uniformly complete then every ideal of finite codimension is uniformly closed. Results of the paper extend (and are motivated by) results of [AL90a,AL90b] and , as well as Kakutani's characterization of closed sublattices of $C(K)$ spaces. |
| title | Uniformly closed sublattices of finite codimension |
| topic | Functional Analysis Primary: 46A40. Secondary: 46B42, 46E05 |
| url | https://arxiv.org/abs/2210.08805 |