Discrete Translates of an Operator in the Schatten $p$-Classes
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913504080953344 |
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| author | Dharra, Bhawna Sivananthan, S. Naidu, D. Venku |
| author_facet | Dharra, Bhawna Sivananthan, S. Naidu, D. Venku |
| contents | In this manuscript, we investigate the properties of systems formed by translations of an operator in the Schatten $p$-classes $\mathcal{T}^p$. We establish the existence of Schauder frames of integer translates in $\mathcal{T}^p$ for $p>2$. Later, we provide an instance of a uniformly discrete $Λ\subset \mathbb{R}^{2d}$ such that there exists an operator whose $Λ$-translates are complete in $\mathcal{T}^p$ for all $p>1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_16757 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Discrete Translates of an Operator in the Schatten $p$-Classes Dharra, Bhawna Sivananthan, S. Naidu, D. Venku Functional Analysis Primary 47B90, Secondary 42C15, 47B10 In this manuscript, we investigate the properties of systems formed by translations of an operator in the Schatten $p$-classes $\mathcal{T}^p$. We establish the existence of Schauder frames of integer translates in $\mathcal{T}^p$ for $p>2$. Later, we provide an instance of a uniformly discrete $Λ\subset \mathbb{R}^{2d}$ such that there exists an operator whose $Λ$-translates are complete in $\mathcal{T}^p$ for all $p>1$. |
| title | Discrete Translates of an Operator in the Schatten $p$-Classes |
| topic | Functional Analysis Primary 47B90, Secondary 42C15, 47B10 |
| url | https://arxiv.org/abs/2311.16757 |