Absolutely $\gamma$ - summing polynomials and the notion of coherence and compatibility

TL;DR

This paper develops an abstract ideal of polynomials, proves it forms a Banach ideal, and investigates the coherence and compatibility of polynomial and multilinear application ideals.

Contribution

It introduces a new abstract ideal of polynomials and analyzes its Banach structure and coherence with multilinear applications, advancing the theoretical framework.

Findings

The abstract ideal of polynomials is a Banach ideal.

The paper establishes coherence between polynomial and multilinear ideals.

It provides a new perspective on the structure of polynomial ideals.

Abstract

In this paper, we construct the abstract ideal of polynomials. We show this is an ideal of Banach and, in a second moment, we explore the question of the coherence and compatibility of the pair composed by the abstract ideals of polynomials and multilinear applications.