New examples of strongly subdifferentiable projective tensor products
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912043911610368 |
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| author | Zoca, Abraham Rueda |
| author_facet | Zoca, Abraham Rueda |
| contents | We prove that the norm of $X\widehat{\otimes}_πY$ is SSD if either $X=\ell_p(I)$ for $p>2$ and $Y$ is a finite-dimensional Banach space such that the modulus of convexity is of power type $q<p$ (e.g. if $Y^*$ is a subspace of $L_q$) or if $X=c_0(I)$ and $Y^*$ is any uniformly convex finite-dimensional Banach space. We also provide a characterisation of SSD elements of a projective tensor product which attain its projective norm in terms of a strengthening of the a local Bollobás property for bilinear mappings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16286 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New examples of strongly subdifferentiable projective tensor products Zoca, Abraham Rueda Functional Analysis We prove that the norm of $X\widehat{\otimes}_πY$ is SSD if either $X=\ell_p(I)$ for $p>2$ and $Y$ is a finite-dimensional Banach space such that the modulus of convexity is of power type $q<p$ (e.g. if $Y^*$ is a subspace of $L_q$) or if $X=c_0(I)$ and $Y^*$ is any uniformly convex finite-dimensional Banach space. We also provide a characterisation of SSD elements of a projective tensor product which attain its projective norm in terms of a strengthening of the a local Bollobás property for bilinear mappings. |
| title | New examples of strongly subdifferentiable projective tensor products |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2409.16286 |