On G(p)-classes of trilinear forms

In a previous paper, the authors laid the foundations of a theory of Schatt en-von Neumann classes G(p) (0 < p less than or equal to infinity) of trili near forms in Hilbert space. This paper continues that research. In the n-d imensional case, it is shown that the best constant (d) over tilde that rel ates the Hilbert-Schmidt norm of a form with its bounded norm behaves like n. Some results are also obtained in the quasi-Banach case (0 < p < 1), and for two-bounded forms. Finally, the domination problem is investigated in the trilinear set-up.