An index of summability for pairs of Banach spaces

TL;DR

This paper introduces a new measure called the index of summability for pairs of Banach spaces, quantifying how far certain polynomials are from being absolutely summing, with some cases where the optimal index is computed.

Contribution

It defines and analyzes the index of summability for pairs of Banach spaces, providing computations of the optimal index in specific cases.

Findings

Defined the index of summability for Banach space pairs

Computed the optimal index in certain cases

Provided insights into the behavior of m-homogeneous polynomials

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.