A Note on Frames in Quaternionic Hilbert Spaces
In this paper, we define a modified version of frame in quaternionic Hilbert spaces (QHS) and give a necessary condition for a block Bessel sequence in terms of a bounded right linear operator. Also, a necessary and sufficient condition for a sequence to be a block Bessel sequence is given. Further...
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| Language: | English |
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University of Maragheh
2025-01-01
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| Series: | Sahand Communications in Mathematical Analysis |
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| Online Access: | https://scma.maragheh.ac.ir/article_717985_5b9511a9b108140afed04985862450ed.pdf |
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| author | Sumit Sharma Raksha Sharma |
| author_facet | Sumit Sharma Raksha Sharma |
| author_sort | Sumit Sharma |
| collection | DOAJ |
| description | In this paper, we define a modified version of frame in quaternionic Hilbert spaces (QHS) and give a necessary condition for a block Bessel sequence in terms of a bounded right linear operator. Also, a necessary and sufficient condition for a sequence to be a block Bessel sequence is given. Further, a method to construct a desired block frame using a given block frame is discussed. Finally, a characterization of block frame in terms of a right linear operator is given. |
| format | Article |
| id | doaj-art-8a5dad161b6146eda643d7f36b7aba18 |
| institution | Kabale University |
| issn | 2322-5807 2423-3900 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj-art-8a5dad161b6146eda643d7f36b7aba182025-02-11T05:28:01ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002025-01-0122112513610.22130/scma.2024.2025108.1666717985A Note on Frames in Quaternionic Hilbert SpacesSumit Sharma0Raksha Sharma1Department of Mathematics, Kirori Mal College, University of Delhi, Delhi 110 007, India.Department of Physics, Kirori Mal College, University of Delhi, Delhi 110 007, India.In this paper, we define a modified version of frame in quaternionic Hilbert spaces (QHS) and give a necessary condition for a block Bessel sequence in terms of a bounded right linear operator. Also, a necessary and sufficient condition for a sequence to be a block Bessel sequence is given. Further, a method to construct a desired block frame using a given block frame is discussed. Finally, a characterization of block frame in terms of a right linear operator is given.https://scma.maragheh.ac.ir/article_717985_5b9511a9b108140afed04985862450ed.pdfframesblock framesquaterninic hilbert space |
| spellingShingle | Sumit Sharma Raksha Sharma A Note on Frames in Quaternionic Hilbert Spaces Sahand Communications in Mathematical Analysis frames block frames quaterninic hilbert space |
| title | A Note on Frames in Quaternionic Hilbert Spaces |
| title_full | A Note on Frames in Quaternionic Hilbert Spaces |
| title_fullStr | A Note on Frames in Quaternionic Hilbert Spaces |
| title_full_unstemmed | A Note on Frames in Quaternionic Hilbert Spaces |
| title_short | A Note on Frames in Quaternionic Hilbert Spaces |
| title_sort | note on frames in quaternionic hilbert spaces |
| topic | frames block frames quaterninic hilbert space |
| url | https://scma.maragheh.ac.ir/article_717985_5b9511a9b108140afed04985862450ed.pdf |
| work_keys_str_mv | AT sumitsharma anoteonframesinquaternionichilbertspaces AT rakshasharma anoteonframesinquaternionichilbertspaces AT sumitsharma noteonframesinquaternionichilbertspaces AT rakshasharma noteonframesinquaternionichilbertspaces |