This is an announcement for the paper “An index of summability for pairs of Banach spaces” by M. Maia, D. Pellegrino and J. Santos.

Abstract: We introduce the notion of index of summability for pairs of Banach spaces; for Banach spaces E; F, this index plays the role of a kind of measure of how the m-homogeneous polynomials from E to F are far from being absolutely summing. In some cases the optimal index of summability is computed.

The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1602.03363