Testing compactness of linear operators
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916496803889152 |
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| author | Hänninen, Timo S. Oikari, Tuomas V. |
| author_facet | Hänninen, Timo S. Oikari, Tuomas V. |
| contents | Let $(F_i)$ be a sequence of sets in a Banach space $X$. For what sequences does the condition
$$ \limsup_{i\to \infty} \sup_{f_i\in F_i} \|Tf_i\|_Y=0 $$ hold for every Banach space $Y$ and every compact operator $T:X\to Y$? We answer this question by giving sufficient (and necessary) criteria for such sequences. We illustrate the applicability of the criteria by examples from literature and by characterizing the $L^p\to L^p$ compactness of dyadic paraproducts on general measure spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17654 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Testing compactness of linear operators Hänninen, Timo S. Oikari, Tuomas V. Functional Analysis Classical Analysis and ODEs Let $(F_i)$ be a sequence of sets in a Banach space $X$. For what sequences does the condition $$ \limsup_{i\to \infty} \sup_{f_i\in F_i} \|Tf_i\|_Y=0 $$ hold for every Banach space $Y$ and every compact operator $T:X\to Y$? We answer this question by giving sufficient (and necessary) criteria for such sequences. We illustrate the applicability of the criteria by examples from literature and by characterizing the $L^p\to L^p$ compactness of dyadic paraproducts on general measure spaces. |
| title | Testing compactness of linear operators |
| topic | Functional Analysis Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2411.17654 |