On G p -Classes of Trilinear Forms
Fernando Cobos, Thomas Kühn, Jaak Peetre · Journal of the London Mathematical Society · 1999
In a previous paper, the authors laid the foundations of a theory of Schatten–von Neumann classes Gp (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 d̂ 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 two-bounded forms. Finally, the domination problem is investigated in the trilinear set-up.