Three kinds of numerical indices of a Banach space II

Abstract

For a Banach space E and a positive integer k, we study about three kinds of numerical indices of E, the multilinear numerical index n^(k) _m (E); the symmetric multilinear numerical index n^(k) _s (E) and the polynomial numerical index n^(k) _p (E). First we show that n^(k) _I (E )≤ n(^(k) _I (E) for I = m; s and present some inequalities among n^(k) _m(E); n^(k) _s(E) and n^(k) _p (E). We also prove that if E is a strictly convex Banach space, then n^(k) _m (E) = 0 for every k ≥2: