Characterization, Dilation, and Perturbation of Basic Continuous Frames
A vector-valued function is called a basic continuous frame if it is a continuous frame for its spanning space. It is shown in this article that basic continuous frames and their oblique duals can be characterized by operators with closed ranges. Furthermore, we show that any oblique dual pair of ba...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/3270281 |
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| _version_ | 1832552301783416832 |
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| author | Xin Zhao Pengtong Li |
| author_facet | Xin Zhao Pengtong Li |
| author_sort | Xin Zhao |
| collection | DOAJ |
| description | A vector-valued function is called a basic continuous frame if it is a continuous frame for its spanning space. It is shown in this article that basic continuous frames and their oblique duals can be characterized by operators with closed ranges. Furthermore, we show that any oblique dual pair of basic continuous frames for a Hilbert space can be dilated to a Type II dual pair for a larger Hilbert space. Finally, a perturbation result for basic continuous frames is given. Since the spanning spaces of two basic continuous frames for a Hilbert space are often different, the research process is more complex than the setting of general continuous frames. |
| format | Article |
| id | doaj-art-7e3cb3bd20f44dccb40b7336c47eb9eb |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-7e3cb3bd20f44dccb40b7336c47eb9eb2025-02-03T05:58:56ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/3270281Characterization, Dilation, and Perturbation of Basic Continuous FramesXin Zhao0Pengtong Li1Department of MathematicsDepartment of MathematicsA vector-valued function is called a basic continuous frame if it is a continuous frame for its spanning space. It is shown in this article that basic continuous frames and their oblique duals can be characterized by operators with closed ranges. Furthermore, we show that any oblique dual pair of basic continuous frames for a Hilbert space can be dilated to a Type II dual pair for a larger Hilbert space. Finally, a perturbation result for basic continuous frames is given. Since the spanning spaces of two basic continuous frames for a Hilbert space are often different, the research process is more complex than the setting of general continuous frames.http://dx.doi.org/10.1155/2022/3270281 |
| spellingShingle | Xin Zhao Pengtong Li Characterization, Dilation, and Perturbation of Basic Continuous Frames Journal of Mathematics |
| title | Characterization, Dilation, and Perturbation of Basic Continuous Frames |
| title_full | Characterization, Dilation, and Perturbation of Basic Continuous Frames |
| title_fullStr | Characterization, Dilation, and Perturbation of Basic Continuous Frames |
| title_full_unstemmed | Characterization, Dilation, and Perturbation of Basic Continuous Frames |
| title_short | Characterization, Dilation, and Perturbation of Basic Continuous Frames |
| title_sort | characterization dilation and perturbation of basic continuous frames |
| url | http://dx.doi.org/10.1155/2022/3270281 |
| work_keys_str_mv | AT xinzhao characterizationdilationandperturbationofbasiccontinuousframes AT pengtongli characterizationdilationandperturbationofbasiccontinuousframes |