On Hilbert–Schmidt Frames for Operators and Riesz Bases
Stable analysis and reconstruction of vectors in closed subspaces of Hilbert spaces can be studied by Gǎvruta's type frame conditions which are related with the concept of atomic systems in separable Hilbert spaces. In this work, first we give Gǎvruta's type frame conditions for a class of...
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| Datum: | 2023 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2023
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| Online Zugang: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1042 |
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| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
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Journal of Mathematical Physics, Analysis, Geometry| Zusammenfassung: | Stable analysis and reconstruction of vectors in closed subspaces of Hilbert spaces can be studied by Gǎvruta's type frame conditions which are related with the concept of atomic systems in separable Hilbert spaces. In this work, first we give Gǎvruta's type frame conditions for a class of Hilbert-Schmidt operators (in short, $\mathcal{C}_2$ class), where a bounded linear operator controls the lower frame condition. We discuss frame-preserving mappings for Hilbert-Schmidt frames for subspaces of a separable Hilbert space. We establish the existence of Hilbert-Schmidt frames for subspaces of the Hilbert-Schmidt class $\mathcal{C}_2$. It is shown that every separable Hilbert space admits a Hilbert-Schmidt frame with respect to a given separable Hilbert space. We obtain necessary and sufficient conditions for Gǎvruta's type frame conditions for sums of Hilbert-Schmidt frames for subspaces. Finally, we discuss Hilbert-Schmidt Riesz bases in separable Hilbert spaces.
Mathematical Subject Classification 2020: 42C15, 42C30, 42C40, 43A32 |
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