Estimating the index of summability of pairs of Banach spaces

Let $E_1,\mathrm{.}\mathrm{.}\mathrm{.},E_m,F$ be Banach spaces. The index of summability of $(E_1\times \cdots \times E_m,F)$ is a kind of measure of how far the $m$-linear operators $T:E_1\times \cdots \times E_m\to F$ are from being multiple summing. In this paper we estimate the index of summability of several pairs of Banach spaces$\mathrm{.}$