Applications of Grothendieck's inequality to linear symplectic geometry

TL;DR

This paper explores how Grothendieck's inequality can be applied to derive bounds on functionals in linear symplectic geometry, demonstrating its usefulness in this mathematical context.

Contribution

It introduces two novel applications of Grothendieck's theorems to establish bounds in symplectic geometry, expanding the toolkit for researchers in the field.

Findings

Established bounds on matrix functionals using Grothendieck's inequality

Demonstrated the effectiveness of factorization theorems in symplectic geometry

Provided new insights into the interplay between functional analysis and symplectic structures

Abstract

Recently in symplectic geometry there arose an interest in bounding various functionals on spaces of matrices. It appears that Grothendieck's theorems about factorization are a useful tool for proving such bounds. In this note we present two such applications.