An integral formula for multiple summing norms of operators

TL;DR

This paper establishes an integral formula for multiple summing norms of multilinear operators on finite-dimensional spaces, leading to new inclusion results, contraction properties, and limit order estimates.

Contribution

It introduces an integral representation for multiple summing norms, enabling new analysis and comparison of multilinear operators in finite-dimensional spaces.

Findings

Integral formula for multiple summing norms

Inclusion and coincidence results for multiple summing mappings

Estimates of limit orders and contraction properties

Abstract

We prove that the multiple summing norm of multilinear operators defined on some $n$-dimensional real or complex vector spaces with the $p$-norm may be written as an integral with respect to stables measures. As an application we show inclusion and coincidence results for multiple summing mappings. We also present some contraction properties and compute or estimate the limit orders of this class of operators.