Subspaces of $\ell_1$ satisfying Grothendieck's theorem

TL;DR

This paper characterizes subspaces of  that satisfy Grothendieck's theorem by examining how nonnegative quadratic forms on these subspaces extend to the entire space.

Contribution

It provides a new characterization of  subspaces satisfying Grothendieck's theorem through extension properties of quadratic forms.

Findings

Identifies conditions for subspaces of  to satisfy Grothendieck's theorem.

Connects quadratic form extension to Grothendieck's property.

Advances understanding of geometric structure of  subspaces.

Abstract

We characterize the subspaces $X$ of $\ell_1$ satisfying Grothendieck's theorem in terms of extension of nonnegative quadratic forms $q:X \longrightarrow \mathbb R$ to the whole $\ell_1$.