Abstract: We characterize all the extreme points of the unit ball in the space of trilinear forms on the Hilbert space C-2. This answers a question posed by R. Grzaslewicz and K. John , who solved the corresponding problem for the real Hilbert space R-2. As an application we determine the best constant in the inequality between the Hilbert-Schmidt norm and the norm of trilinear forms.
Keywords: Trilinear form;
norm; Hilbert-Schmidt norm; extreme point; extreme point of unit ball