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

Published 1 Jun 2026 in math.FA | (2606.01675v1)

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_p2)=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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