Ideals of polynomials between Banach spaces revisited

Abstract

Ideals of polynomials and multilinear operators between Banach spaces have been exhaustively investigated in the last decades. In this paper, we introduce a unified (and more general) approach and propose some lines of investigation in this new framework. Among other results, we prove a Bohnenblust-Hille inequality in this more general setting. Contents 1. Introduction 1 2. Ideals of polynomials and multilinear operators: the classic definitions 2 3. Basic results 4 4. The unified approach: multipolynomial ideals 8 5. Multipolynomial hyper-ideals 10 6. A Bohnenblust-Hille inequality for multipolynomials 13 References 16