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 frame...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Maragheh
2019-07-01
|
| Series: | Sahand Communications in Mathematical Analysis |
| Subjects: | |
| Online Access: | http://scma.maragheh.ac.ir/article_35726_cc21d1f5aa898076fe219206175ae0ca.pdf |
| _version_ | 1811195335955972096 |
|---|---|
| author | Morteza Mirzaee Azandaryani |
| author_facet | Morteza Mirzaee Azandaryani |
| author_sort | Morteza Mirzaee Azandaryani |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-12T00:40:28Z |
| format | Article |
| id | doaj.art-6aa75f1ee894426381182551b8398948 |
| institution | Directory Open Access Journal |
| issn | 2322-5807 2423-3900 |
| language | English |
| last_indexed | 2024-04-12T00:40:28Z |
| publishDate | 2019-07-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj.art-6aa75f1ee894426381182551b83989482022-12-22T03:55:00ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002019-07-0115113514610.22130/scma.2018.81624.39635726Approximate Duals of $g$-frames and Fusion Frames in Hilbert $C^ast-$modulesMorteza Mirzaee Azandaryani0Department of Mathematics, University of Qom, Qom, Iran.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.http://scma.maragheh.ac.ir/article_35726_cc21d1f5aa898076fe219206175ae0ca.pdfFrame$g$-frameFusion frameBiorthogonal sequenceApproximate duality |
| spellingShingle | Morteza Mirzaee Azandaryani Approximate Duals of $g$-frames and Fusion Frames in Hilbert $C^ast-$modules Sahand Communications in Mathematical Analysis Frame $g$-frame Fusion frame Biorthogonal sequence Approximate duality |
| title | Approximate Duals of $g$-frames and Fusion Frames in Hilbert $C^ast-$modules |
| title_full | Approximate Duals of $g$-frames and Fusion Frames in Hilbert $C^ast-$modules |
| title_fullStr | Approximate Duals of $g$-frames and Fusion Frames in Hilbert $C^ast-$modules |
| title_full_unstemmed | Approximate Duals of $g$-frames and Fusion Frames in Hilbert $C^ast-$modules |
| title_short | Approximate Duals of $g$-frames and Fusion Frames in Hilbert $C^ast-$modules |
| title_sort | approximate duals of g frames and fusion frames in hilbert c ast modules |
| topic | Frame $g$-frame Fusion frame Biorthogonal sequence Approximate duality |
| url | http://scma.maragheh.ac.ir/article_35726_cc21d1f5aa898076fe219206175ae0ca.pdf |
| work_keys_str_mv | AT mortezamirzaeeazandaryani approximatedualsofgframesandfusionframesinhilbertcastmodules |