{"title":"Hilbert $C^ast-$模中$g$-框架和$融合框架的近似对偶","authors":"M. M. Azandaryani","doi":"10.22130/SCMA.2018.81624.396","DOIUrl":null,"url":null,"abstract":"In this paper, we study approximate duals of $g$-frames and fusion frames in Hilbert $C^ast-$modules. We get some relations between approximate duals of $g$-frames and biorthogonal Bessel sequences, and using these relations, some results for approximate duals of modular Riesz bases and fusion frames are obtained. Moreover, we generalize the concept of $Q-$approximate duality of $g$-frames and fusion frames to Hilbert $C^ast-$modules, where $Q$ is an adjointable operator, and obtain some properties of this kind of approximate duals.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"15 1","pages":"135-146"},"PeriodicalIF":0.0000,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Approximate Duals of $g$-frames and Fusion Frames in Hilbert $C^ast-$modules\",\"authors\":\"M. M. Azandaryani\",\"doi\":\"10.22130/SCMA.2018.81624.396\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we study approximate duals of $g$-frames and fusion frames in Hilbert $C^ast-$modules. We get some relations between approximate duals of $g$-frames and biorthogonal Bessel sequences, and using these relations, some results for approximate duals of modular Riesz bases and fusion frames are obtained. Moreover, we generalize the concept of $Q-$approximate duality of $g$-frames and fusion frames to Hilbert $C^ast-$modules, where $Q$ is an adjointable operator, and obtain some properties of this kind of approximate duals.\",\"PeriodicalId\":38924,\"journal\":{\"name\":\"Communications in Mathematical Analysis\",\"volume\":\"15 1\",\"pages\":\"135-146\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Mathematical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22130/SCMA.2018.81624.396\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22130/SCMA.2018.81624.396","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Approximate Duals of $g$-frames and Fusion Frames in Hilbert $C^ast-$modules
In this paper, we study approximate duals of $g$-frames and fusion frames in Hilbert $C^ast-$modules. We get some relations between approximate duals of $g$-frames and biorthogonal Bessel sequences, and using these relations, some results for approximate duals of modular Riesz bases and fusion frames are obtained. Moreover, we generalize the concept of $Q-$approximate duality of $g$-frames and fusion frames to Hilbert $C^ast-$modules, where $Q$ is an adjointable operator, and obtain some properties of this kind of approximate duals.