{"title":"论希尔伯特 $$C^*$$ 模块的 $$^*$$ 融合框架","authors":"Nadia Assila, Samir Kabbaj, Hicham Zoubeir","doi":"10.1007/s43036-024-00337-6","DOIUrl":null,"url":null,"abstract":"<div><p>Our paper aims to extend fusion frames to Hilbert C<span>\\(^{*}\\)</span>-modules. We introduce <span>\\(^*\\)</span>-fusion frames associated to weighted sequences of closed orthogonally complemented submodules, showcasing similarities to Hilbert space frames. Using Dragan S. Djordjevic’s distance, we define submodule angles and establish a new topology on the set of sequences of closed orthogonally complemented submodules. Relying on this topology, we obtain for our <span>\\(^*\\)</span>-fusion frames, some new perturbation results of topological and geometric character.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 2","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On \\\\(^*\\\\)-fusion frames for Hilbert \\\\(C^*\\\\)-modules\",\"authors\":\"Nadia Assila, Samir Kabbaj, Hicham Zoubeir\",\"doi\":\"10.1007/s43036-024-00337-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Our paper aims to extend fusion frames to Hilbert C<span>\\\\(^{*}\\\\)</span>-modules. We introduce <span>\\\\(^*\\\\)</span>-fusion frames associated to weighted sequences of closed orthogonally complemented submodules, showcasing similarities to Hilbert space frames. Using Dragan S. Djordjevic’s distance, we define submodule angles and establish a new topology on the set of sequences of closed orthogonally complemented submodules. Relying on this topology, we obtain for our <span>\\\\(^*\\\\)</span>-fusion frames, some new perturbation results of topological and geometric character.</p></div>\",\"PeriodicalId\":44371,\"journal\":{\"name\":\"Advances in Operator Theory\",\"volume\":\"9 2\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-04-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Operator Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s43036-024-00337-6\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Operator Theory","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s43036-024-00337-6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
我们的论文旨在将融合框架扩展到希尔伯特 C（^{*}\）模块。我们引入了与封闭正交互补子模的加权序列相关联的（^**）融合框架，展示了与希尔伯特空间框架的相似性。利用 Dragan S. Djordjevic 的距离，我们定义了子模角，并在封闭的正交互补子模序列集合上建立了新的拓扑学。依靠这个拓扑，我们为我们的 \(^*\)-fusion 框架得到了一些拓扑和几何性质的新扰动结果。
On \(^*\)-fusion frames for Hilbert \(C^*\)-modules
Our paper aims to extend fusion frames to Hilbert C\(^{*}\)-modules. We introduce \(^*\)-fusion frames associated to weighted sequences of closed orthogonally complemented submodules, showcasing similarities to Hilbert space frames. Using Dragan S. Djordjevic’s distance, we define submodule angles and establish a new topology on the set of sequences of closed orthogonally complemented submodules. Relying on this topology, we obtain for our \(^*\)-fusion frames, some new perturbation results of topological and geometric character.
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