Estimating the index of summability of pairs of Banach spaces

TL;DR

This paper investigates a measure called the index of summability for m-linear operators between Banach spaces, providing estimates for various pairs to understand their proximity to multiple summing operators.

Contribution

It introduces estimates for the index of summability for pairs of Banach spaces, advancing understanding of multilinear operator behavior.

Findings

Derived bounds for the index of summability in specific Banach space pairs

Provided new estimates that quantify how close operators are to being multiple summing

Enhanced the theoretical framework for analyzing multilinear operators in 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 $T:E_{1}\times\cdots\times E_{m}\rightarrow F$ are from being multiple summing. In this paper we estimate the index of summability of several pairs of Banach spaces$.$