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arXiv · 2606.01675

The Numerical Index of Two-Dimensional Real $\ell_p$ Spaces

Rafael Chiclana
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Abstract

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.

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Rafael Chiclana. 2026-06-01. The Numerical Index of Two-Dimensional Real $\ell_p$ Spaces. https://arxiv.org/abs/2606.01675

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