Composition ideals of Lip-Linear operators and a Hilbert space characterization
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916829526491136 |
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| author | Ferradi, Athmane Saadi, Khalil |
| author_facet | Ferradi, Athmane Saadi, Khalil |
| contents | In this paper, we investigate classes of Lip-linear operators constructed using the composition ideal method. We focus on two fundamental linear operator ideals, $p$-summing and strongly $p$-summing operators, and extend them to define the corresponding classes of Lip-linear operators. Several key results are established, including a characterization theorem for Hilbert spaces originally due to Kwapień. Specifically, we show that a Banach space $F$ is isomorphic to a Hilbert space if and only if every factorable strongly $p$-summing Lip-linear operator with values in $F$ is Cohen strongly $p$-summing. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_04492 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Composition ideals of Lip-Linear operators and a Hilbert space characterization Ferradi, Athmane Saadi, Khalil Functional Analysis 47B10, 46B28, 47L20 In this paper, we investigate classes of Lip-linear operators constructed using the composition ideal method. We focus on two fundamental linear operator ideals, $p$-summing and strongly $p$-summing operators, and extend them to define the corresponding classes of Lip-linear operators. Several key results are established, including a characterization theorem for Hilbert spaces originally due to Kwapień. Specifically, we show that a Banach space $F$ is isomorphic to a Hilbert space if and only if every factorable strongly $p$-summing Lip-linear operator with values in $F$ is Cohen strongly $p$-summing. |
| title | Composition ideals of Lip-Linear operators and a Hilbert space characterization |
| topic | Functional Analysis 47B10, 46B28, 47L20 |
| url | https://arxiv.org/abs/2507.04492 |