Author

D. Pellegrino

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Preprint Sep 2026

Symmetric Kahane--Salem--Zygmund Inequalities and the Supremum Norm

The Kahane--Salem--Zygmund inequality provides unimodular $m$-linear forms with small supremum norm. We consider its dimension-free symmetric constant $C_m^{\mathrm{sym}}$ over the real scalar field, defined by the requirement that, for every $n$, some real symmetric unimodular $m$-linear form $A:(\ell_\infty^n)^m\to\m...

D. Pellegrino, A. Raposo, Eduardo V. Teixeira · 0 citations

Preprint Sep 2026

The phase diagram of injective-to-projective tensor distortion

For finite-dimensional Banach spaces $E$ and $F$, set \[ \rho(E,F):=\sup_{0\neq z\in E\otimes F}\frac{\pi(z)}{\varepsilon(z)}. \] The square growth of $\rho(\ell_p^d,\ell_q^d)$ was determined by Bonet, Defant, Peris and Ramanujan. We study the rectangular problem with the two dimensions varying independently. If $r=\mi...

D. Núñez-Alarcón, D. Pellegrino, J. Santos · 0 citations

Preprint Aug 2026

The Aron--Rueda zero-subspace problem

We determine the exact finite-dimensional threshold in the zero-subspace problem of Aron and Rueda for complex homogeneous polynomials. More precisely, for every $d$ and $k$ we determine the least $m$ such that every $d$-homogeneous polynomial on $\mathbb{C}^m$ vanishes on a $k$-dimensional linear subspace. We also det...

N. Albuquerque, D. Pellegrino, A. Raposo · 0 citations