On G(p)-classes of trilinear forms

Abstract

In a previous paper, the authors laid the foundations of a theory of Schatten±von Neumann classes 'p (0!p%¢) of trilinear forms in Hilbert space. This paper continues that research. In the n-dimensional case, it is shown that the best constant d# that relates 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 twobounded forms. Finally, the domination problem is investigated in the trilinear set-up.