Constructing hyper-ideals of multilinear operators between Banach spaces

TL;DR

This paper introduces two novel methods for constructing hyper-ideals of multilinear operators between Banach spaces, expanding the classes of such operators and establishing some as Banach or p-Banach hyper-ideals.

Contribution

The paper develops two new methods for constructing hyper-ideals, overcoming limitations of classical approaches and identifying new classes of multilinear operators.

Findings

Some well-studied classes are Banach hyper-ideals.

New classes of multilinear operators are generated.

Methods demonstrate the existence of p-Banach hyper-ideals.

Abstract

In view of the fact that some classical methods to construct multi-ideals fail in constructing hyper-ideals, in this paper we develop two new methods to construct hyper-ideals of multilinear operators between Banach spaces. These methods generate new classes of multilinear operators and show that some important well studied classes are Banach or p-Banach hyper-ideals.