Estimating the index of summability of pairs of Banach spaces

Abstract

Let $E_1,...,E_m,F$ be Banach spaces. The index of summability of $\left(E_1\times \cdots \times E_m,F\right)$ 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$.$