Grothendieck's inequality in the noncommutative Schwartz space
  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 Fr\'echet algebra of smooth operators. These hold in non-optimal form by a simple nuclearity argument. We obtain optimal versions and reformulate the inequalities in several different ways. 
Rupert H. Levene and Krzysztof Piszczek
math.FA math.OA