Hyper-ideals of multilinear operators and two-sided polynomial ideals generated by sequence classes

TL;DR

This paper introduces a new technique for constructing hyper-ideals and two-sided polynomial ideals in the nonlinear setting of multilinear operators and polynomials, expanding the understanding of their structure in Banach spaces.

Contribution

It develops a sequence transformation method to generate new hyper-ideals and polynomial two-sided ideals, and demonstrates that many known ideals are actually hyper-ideals or two-sided ideals.

Findings

New technique for creating hyper-ideals and two-sided ideals

Identification of well-studied ideals as hyper-ideals or two-sided ideals

Enhanced understanding of the structure of nonlinear operator ideals

Abstract

In the nonlinear field of multilinear operators and homogeneous polynomials between Banach spaces, we develop a technique, based on the transformation of vector-valued sequences, to create new examples of hyper-ideals of multilinear operators, polynomial hyper-ideals and polynomial two-sided ideals. Several well studied ideals are shown to be actually hyper-ideals or two-sided ideals.