# Diagonal Multilinear Operators on K\"othe Sequence Spaces

## TL;DR

This paper explores the structure of diagonal multilinear operators on K"othe sequence spaces, establishing new relationships with multiplier spaces and extending summing operator ideals to multilinear contexts.

## Contribution

It introduces a novel analysis of multilinear ideals on K"othe sequence spaces and extends the concept of absolutely summing operators to multilinear mappings.

## Key findings

- Characterization of diagonal multilinear operators on Lorentz sequence spaces.
- Relationships between multilinear ideals and multiplier spaces.
- Extension of absolutely summing operators to multilinear mappings.

## Abstract

We analyze the interplay between maximal/minimal/adjoint ideals of multilinear operators (between sequence spaces) and their associated K\"othe sequence spaces. We establish relationships with spaces of multipliers and apply these results to describe diagonal multilinear operators from Lorentz sequence spaces. We also define and study some properties of the ideal of $(E;p)$-summing multilinear mappings, a natural extension of the linear ideal of absolutely $(E;p)$-summing operators.