| dc.creator | El Idrissi, Nizar | |
| dc.creator | Kabbaj, Samir | |
| dc.creator | Moalige, Brahim | |
| dc.date | 2023-05-09 | |
| dc.date.accessioned | 2023-05-11T20:42:08Z | |
| dc.date.available | 2023-05-11T20:42:08Z | |
| dc.identifier | https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4818 | |
| dc.identifier | 10.22199/issn.0717-6279-4818 | |
| dc.identifier.uri | https://revistaschilenas.uchile.cl/handle/2250/225567 | |
| dc.description | If H is a Hilbert space, the non-compact Stiefel manifold St(n, H) consists of independent n-tuples in H. In this article, we contribute to the topological study of non-compact Stiefel manifolds, mainly by proving two results on the path-connectedness and topological closure of some sets related to the non-compact Stiefel manifold. In the first part, after introducing and proving an essential lemma, we prove that ∩j∈J (U(j) + St(n, H)) is path-connected by polygonal paths under a condition on the codimension of the span of the components of the translating J-family. Then, in the second part, we show that the topological closure of St(n, H)∩S contains all polynomial paths contained in S and passing through a point in St(n, H). As a consequence, we prove that St(n, H) is relatively dense in a certain class of subsets which we illustrate with many examples from frame theory coming from the study of the solutions of some linear and quadratic equations which are finite-dimensional continuous frames. Since St(n, L2(X, μ; F)) is isometric to, FF(X, μ), n, this article is also a contribution to the theory of finite-dimensional continuous Hilbert space frames. | en-US |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.publisher | Universidad Católica del Norte. | en-US |
| dc.relation | https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4818/4287 | |
| dc.rights | Copyright (c) 2023 Nizar El Idrissi, Samir Kabbaj, Brahim Moalige | en-US |
| dc.rights | https://creativecommons.org/licenses/by/4.0 | en-US |
| dc.source | Proyecciones (Antofagasta, On line); Vol. 42 No. 3 (2023); 571-597 | en-US |
| dc.source | Proyecciones. Revista de Matemática; Vol. 42 Núm. 3 (2023); 571-597 | es-ES |
| dc.source | 0717-6279 | |
| dc.source | 10.22199/issn.0717-6279-2023-03 | |
| dc.subject | Stiefel manifold | en-US |
| dc.subject | continuous frame | en-US |
| dc.subject | path-connected space | en-US |
| dc.subject | topological closure | en-US |
| dc.subject | dense subset | en-US |
| dc.subject | 57N20 | en-US |
| dc.subject | 42C15 | en-US |
| dc.subject | 54D05 | en-US |
| dc.subject | 54D99 | en-US |
| dc.title | Path-connectedness and topological closure of some sets related to the non-compact Stiefel manifold | en-US |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
| dc.type | Peer-reviewed Article | en-US |
| dc.type | text | en-US |
