On the representation of multi-ideals by tensor norms

TL;DR

This paper investigates how multi-ideals and ideals of multilinear forms can be represented using smooth tensor norms, providing insights into their structural properties.

Contribution

It introduces a framework for representing multi-ideals via smooth tensor norms, extending the understanding of tensor norm applications in multilinear analysis.

Findings

Characterization of smooth tensor norms

Representation results for multi-ideals

Connections between tensor norms and multilinear forms

Abstract

A tensor norm $\beta= (\beta_{n})_{n=1}^{\infty}$ is smooth if the natural correspondence $(E_{1} \otimes\cdots\otimes E_{n} \otimes\mathbb{K},\beta_{n+1}) \longleftrightarrow (E_{1} \otimes\cdots\otimes E_{n} ,\beta_{n})$ is always an isometric isomorphism. In this paper we study the representation of multi-ideals and of ideals of multilinear forms by smooth tensor norms.