Product spaces generated by bilinear maps and duality

TL;DR

This paper explores a duality-based framework for product spaces of Banach spaces, unifying various constructions in functional analysis through an abstract notion of multiplication operators.

Contribution

It introduces a duality-driven approach to defining product spaces of Banach spaces, linking them to multiplication operators and unifying multiple existing constructions.

Findings

Provides a duality-based definition of Banach space products

Connects product space constructions to multiplication operators

Includes relevant examples and applications in functional analysis

Abstract

We analyze a definition of product of Banach spaces that is naturally associated by duality with an abstract notion of space of multiplication operators. This dual relation allows to understand several constructions coming from different fields of the functional analysis, that can be seen as instances of the abstract one when a particular product is considered. Some relevant examples and applications are shown.