On $K$-frames for Quaternionic Hilbert Spaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910687108792320 |
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| author | Khachiaa, Najib |
| author_facet | Khachiaa, Najib |
| contents | The aim of this paper is to study $K$-frames for quaternionic Hilbert spaces. First, we present the quaternionic version of Douglas's theorem and then investigate $K$-frames for a quaternionic Hilbert space $\mathcal{H}$, where $K \in \mathbb{B}(\mathcal{H})$. Given two quaternionic Hilbert spaces $\mathcal{H}_1$ and $\mathcal{H}_2$, along with two right $\mathbb{H}$-linear bounded operators $K_1 \in \mathbb{B}(\mathcal{H}_1)$ and $K_2 \in \mathbb{B}(\mathcal{H}_2)$, we study the $K_1 \oplus K_2$-frames for the super space $\mathcal{H}_1 \oplus \mathcal{H}_2$ and their relationship with $K_1$-frames and $K_2$-frames for $\mathcal{H}_1$ and $\mathcal{H}_2$, respectively. We also explore the $K_1 \oplus K_2$-duality in relation to $K_1$-duality and $K_2$-duality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04154 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On $K$-frames for Quaternionic Hilbert Spaces Khachiaa, Najib Functional Analysis 42C15, 42C40, 47A05 The aim of this paper is to study $K$-frames for quaternionic Hilbert spaces. First, we present the quaternionic version of Douglas's theorem and then investigate $K$-frames for a quaternionic Hilbert space $\mathcal{H}$, where $K \in \mathbb{B}(\mathcal{H})$. Given two quaternionic Hilbert spaces $\mathcal{H}_1$ and $\mathcal{H}_2$, along with two right $\mathbb{H}$-linear bounded operators $K_1 \in \mathbb{B}(\mathcal{H}_1)$ and $K_2 \in \mathbb{B}(\mathcal{H}_2)$, we study the $K_1 \oplus K_2$-frames for the super space $\mathcal{H}_1 \oplus \mathcal{H}_2$ and their relationship with $K_1$-frames and $K_2$-frames for $\mathcal{H}_1$ and $\mathcal{H}_2$, respectively. We also explore the $K_1 \oplus K_2$-duality in relation to $K_1$-duality and $K_2$-duality. |
| title | On $K$-frames for Quaternionic Hilbert Spaces |
| topic | Functional Analysis 42C15, 42C40, 47A05 |
| url | https://arxiv.org/abs/2411.04154 |