Grothendieck’s inequality in the noncommutative Schwartz space
Volume 234 / 2016
Studia Mathematica 234 (2016), 185-194
MSC: Primary 47A30, 47A07, 47L10; Secondary 47A63.
DOI: 10.4064/sm8552-6-2016
Published online: 23 August 2016
Abstract
In the spirit of Grothendieck’s famous inequality from the theory of Banach spaces, we study a sequence of inequalities for the noncommutative Schwartz space, a Fréchet algebra of smooth operators. These hold in nonoptimal form by a simple nuclearity argument. We obtain optimal versions and reformulate the inequalities in several different ways.
