The Numerical Index of Two-Dimensional Real $\ell_p$ Spaces
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910279648935936 |
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| author | Chiclana, Rafael |
| author_facet | Chiclana, Rafael |
| contents | The computation of the numerical index of classical Banach spaces is one of the original problems in the theory. In this paper, we compute the numerical index of two-dimensional real \(\ell_p\)-spaces for all \(p\ge1\). More precisely, we prove that \[ n(\ell_p^2)=v(J), \qquad J= \begin{pmatrix}
0&1
-1&0 \end{pmatrix}, \] confirming the conjectured formula in the two-dimensional real case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_01675 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Numerical Index of Two-Dimensional Real $\ell_p$ Spaces Chiclana, Rafael Functional Analysis 47A12, 46B20, 46B04 The computation of the numerical index of classical Banach spaces is one of the original problems in the theory. In this paper, we compute the numerical index of two-dimensional real \(\ell_p\)-spaces for all \(p\ge1\). More precisely, we prove that \[ n(\ell_p^2)=v(J), \qquad J= \begin{pmatrix} 0&1 -1&0 \end{pmatrix}, \] confirming the conjectured formula in the two-dimensional real case. |
| title | The Numerical Index of Two-Dimensional Real $\ell_p$ Spaces |
| topic | Functional Analysis 47A12, 46B20, 46B04 |
| url | https://arxiv.org/abs/2606.01675 |