On Sum and Stability of Continuous $G$-Frames
In this paper, we give some conditions under which the finite sum of continuous $g$-frames is again a continuous $g$-frame. We give necessary and sufficient conditions for the continuous $g$-frames $Lambda=left{Lambda_w in Bleft(H,K_wright): win Omegaright}$ and $Gamma=left{Gamma_w in Bleft(H,K_wrig...
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| Format: | Article |
| Language: | English |
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University of Maragheh
2020-01-01
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| Series: | Sahand Communications in Mathematical Analysis |
| Subjects: | |
| Online Access: | http://scma.maragheh.ac.ir/article_37340_62593c31158dad0ce79ce0e6381dd264.pdf |
| _version_ | 1818487877925863424 |
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| author | Azam Yousefzadeheyni Mohammad Reza Abdollahpour |
| author_facet | Azam Yousefzadeheyni Mohammad Reza Abdollahpour |
| author_sort | Azam Yousefzadeheyni |
| collection | DOAJ |
| description | In this paper, we give some conditions under which the finite sum of continuous $g$-frames is again a continuous $g$-frame. We give necessary and sufficient conditions for the continuous $g$-frames $Lambda=left{Lambda_w in Bleft(H,K_wright): win Omegaright}$ and $Gamma=left{Gamma_w in Bleft(H,K_wright): win Omegaright}$ and operators $U$ and $V$ on $H$ such that $Lambda U+Gamma V={Lambda_w U+Gamma_w V in Bleft(H,K_wright): win Omega}$ is again a continuous $g$-frame. Moreover, we obtain some sufficient conditions under which the finite sum of continuous $g$-frames are stable under small perturbations. |
| first_indexed | 2024-12-10T16:44:00Z |
| format | Article |
| id | doaj.art-180e2d67fc68466db0a52eb6f5437506 |
| institution | Directory Open Access Journal |
| issn | 2322-5807 2423-3900 |
| language | English |
| last_indexed | 2024-12-10T16:44:00Z |
| publishDate | 2020-01-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj.art-180e2d67fc68466db0a52eb6f54375062022-12-22T01:41:06ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002020-01-0117115716910.22130/scma.2018.90101.47237340On Sum and Stability of Continuous $G$-FramesAzam Yousefzadeheyni0Mohammad Reza Abdollahpour1Department of Mathematics, Faculty of Science, University of Mohaghegh Ardabili, 56199-11367, Ardabil, Iran.Department of Mathematics, Faculty of Science, University of Mohaghegh Ardabili, 56199-11367, Ardabil, Iran.In this paper, we give some conditions under which the finite sum of continuous $g$-frames is again a continuous $g$-frame. We give necessary and sufficient conditions for the continuous $g$-frames $Lambda=left{Lambda_w in Bleft(H,K_wright): win Omegaright}$ and $Gamma=left{Gamma_w in Bleft(H,K_wright): win Omegaright}$ and operators $U$ and $V$ on $H$ such that $Lambda U+Gamma V={Lambda_w U+Gamma_w V in Bleft(H,K_wright): win Omega}$ is again a continuous $g$-frame. Moreover, we obtain some sufficient conditions under which the finite sum of continuous $g$-frames are stable under small perturbations.http://scma.maragheh.ac.ir/article_37340_62593c31158dad0ce79ce0e6381dd264.pdfcontinuous $g$-frameparseval continuous $g$-framecontinuous $g$-bessel familystability |
| spellingShingle | Azam Yousefzadeheyni Mohammad Reza Abdollahpour On Sum and Stability of Continuous $G$-Frames Sahand Communications in Mathematical Analysis continuous $g$-frame parseval continuous $g$-frame continuous $g$-bessel family stability |
| title | On Sum and Stability of Continuous $G$-Frames |
| title_full | On Sum and Stability of Continuous $G$-Frames |
| title_fullStr | On Sum and Stability of Continuous $G$-Frames |
| title_full_unstemmed | On Sum and Stability of Continuous $G$-Frames |
| title_short | On Sum and Stability of Continuous $G$-Frames |
| title_sort | on sum and stability of continuous g frames |
| topic | continuous $g$-frame parseval continuous $g$-frame continuous $g$-bessel family stability |
| url | http://scma.maragheh.ac.ir/article_37340_62593c31158dad0ce79ce0e6381dd264.pdf |
| work_keys_str_mv | AT azamyousefzadeheyni onsumandstabilityofcontinuousgframes AT mohammadrezaabdollahpour onsumandstabilityofcontinuousgframes |