Results on Continuous $K$-frames for Quaternionic (Super) Hilbert Spaces
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912116357726208 |
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| author | Khachiaa, Najib |
| author_facet | Khachiaa, Najib |
| contents | This paper aims to explore the concept of continuous \( K \)-frames in quaternionic Hilbert spaces. First, we investigate \( K \)-frames in a single quaternionic Hilbert space \( \mathcal{H} \), where \( K \) is a right $\mathbb{H}$-linear bounded operator acting on \( \mathcal{H} \). Then, we extend the research to two quaternionic Hilbert spaces, \( \mathcal{H}_1 \) and \( \mathcal{H}_2 \), and study \( K_1 \oplus K_2 \)-frames for the super quaternionic Hilbert space \( \mathcal{H}_1 \oplus \mathcal{H}_2 \), where \( K_1 \) and \( K_2 \) are right $\mathbb{H}$-linear bounded operators on \( \mathcal{H}_1 \) and \( \mathcal{H}_2 \), respectively. We examine the relationship between the continuous \( K_1 \oplus K_2 \)-frames and the continuous \( K_1 \)-frames for \( \mathcal{H}_1 \) and the continuous \( K_2 \)-frames for \( \mathcal{H}_2 \). Additionally, we explore the duality between the continuous \( K_1 \oplus K_2 \)-frames and the continuous \( K_1 \)- and \( K_2 \)-frames individually. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07937 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Results on Continuous $K$-frames for Quaternionic (Super) Hilbert Spaces Khachiaa, Najib Functional Analysis 42C15, 42C40, 47A05 This paper aims to explore the concept of continuous \( K \)-frames in quaternionic Hilbert spaces. First, we investigate \( K \)-frames in a single quaternionic Hilbert space \( \mathcal{H} \), where \( K \) is a right $\mathbb{H}$-linear bounded operator acting on \( \mathcal{H} \). Then, we extend the research to two quaternionic Hilbert spaces, \( \mathcal{H}_1 \) and \( \mathcal{H}_2 \), and study \( K_1 \oplus K_2 \)-frames for the super quaternionic Hilbert space \( \mathcal{H}_1 \oplus \mathcal{H}_2 \), where \( K_1 \) and \( K_2 \) are right $\mathbb{H}$-linear bounded operators on \( \mathcal{H}_1 \) and \( \mathcal{H}_2 \), respectively. We examine the relationship between the continuous \( K_1 \oplus K_2 \)-frames and the continuous \( K_1 \)-frames for \( \mathcal{H}_1 \) and the continuous \( K_2 \)-frames for \( \mathcal{H}_2 \). Additionally, we explore the duality between the continuous \( K_1 \oplus K_2 \)-frames and the continuous \( K_1 \)- and \( K_2 \)-frames individually. |
| title | Results on Continuous $K$-frames for Quaternionic (Super) Hilbert Spaces |
| topic | Functional Analysis 42C15, 42C40, 47A05 |
| url | https://arxiv.org/abs/2411.07937 |