ISOMETRIC CHARACTERIZATION OF L(P)(N) SPACES

The paper establishes some characterizations of l(p)n spaces in terms of p-summing or p-nuclear norms of the identity operator on the given space E. In particular, for an n-dimensional Banach space E and 1 less -than-or-equal-to p < 2, E is isometric to l(p)n if and only if pi(p)( E) greater-than-or-equal-to n1/P and E* has cotype p' with the consta nt one. Furthermore, l(p)n spaces are characterized by inequalities fo r p-summing norms of operators related to the John's ellipsoid of maxi mal volume contained in the unit ball