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| Principais autores: | , , , , |
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| Formato: | Preprint |
| Publicado em: |
2026
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| Assuntos: | |
| Acesso em linha: | https://arxiv.org/abs/2602.23796 |
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| _version_ | 1866910034901860352 |
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| author | Aliaga, Ramón J. Dantas, Sheldon Guerrero-Viu, Juan Jung, Mingu Roldán, Óscar |
| author_facet | Aliaga, Ramón J. Dantas, Sheldon Guerrero-Viu, Juan Jung, Mingu Roldán, Óscar |
| contents | We introduce a Bochner integral approach to projective norm attainment in tensor products of Banach spaces by defining the class of integral projective norm-attaining tensors. This framework provides a broader, measure-theoretic approach to the study of projective norm attainment in tensor products of Banach spaces. We show that every integral norm-attaining tensor can be approximated in norm by norm-attaining tensors with finite representations. As a consequence, the Bishop-Phelps type density problem for classical norm-attaining tensors is equivalent to the corresponding density problem for integral norm-attaining tensors. Moreover, we prove that if an integral projective norm-attaining tensor represented by a Radon measure is an extreme point, then it must be an elementary tensor. We further investigate weaker topological versions of integral norm-attainment, including weak and weak$^*$ integral representations, providing sufficient conditions for the existence of Bochner representations. Finally, we extend known constructions of projective tensor products containing non-norm-attaining tensors to the integral setting. We show, for instance, that $L_1\widehat{\otimes}_πL_p$ and the real $c_0\widehat{\otimes}_πL_p$ contain non-norm-attaining tensors for $1<p<\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23796 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Integral representations of projective norm-attaining tensors Aliaga, Ramón J. Dantas, Sheldon Guerrero-Viu, Juan Jung, Mingu Roldán, Óscar Functional Analysis We introduce a Bochner integral approach to projective norm attainment in tensor products of Banach spaces by defining the class of integral projective norm-attaining tensors. This framework provides a broader, measure-theoretic approach to the study of projective norm attainment in tensor products of Banach spaces. We show that every integral norm-attaining tensor can be approximated in norm by norm-attaining tensors with finite representations. As a consequence, the Bishop-Phelps type density problem for classical norm-attaining tensors is equivalent to the corresponding density problem for integral norm-attaining tensors. Moreover, we prove that if an integral projective norm-attaining tensor represented by a Radon measure is an extreme point, then it must be an elementary tensor. We further investigate weaker topological versions of integral norm-attainment, including weak and weak$^*$ integral representations, providing sufficient conditions for the existence of Bochner representations. Finally, we extend known constructions of projective tensor products containing non-norm-attaining tensors to the integral setting. We show, for instance, that $L_1\widehat{\otimes}_πL_p$ and the real $c_0\widehat{\otimes}_πL_p$ contain non-norm-attaining tensors for $1<p<\infty$. |
| title | Integral representations of projective norm-attaining tensors |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2602.23796 |