Linear structure in certain subsets of quasi-Banach sequence spaces

For 0 < p < 1, we prove that there is a c-dimensional subspace of L(l(p), l(p)) such that, except for the null vector, all of its vectors fail to be absolutely (r, s)-summing regardless of the real numbers r, s, with 1 <= s <= r < infinity. This extends a result proved by Maddox in 1987. Moreover, the result is sharp in the sense that it is not valid for p >= 1.