Projective and injective tensor products of Banach $L^0$-modules

TL;DR

This paper explores the properties of projective and injective tensor products within Banach $L^0$-modules over measure spaces, extending key analytical tools to this context.

Contribution

It introduces extensions of quotient operators, summable families, and Schauder bases to Banach $L^0$-modules, advancing the theoretical framework.

Findings

Extended quotient operators to Banach $L^0$-modules

Developed summable families in this setting

Analyzed tensor product structures and properties

Abstract

We study projective and injective tensor products of Banach $L^0$-modules over a $\sigma$-finite measure space. En route, we extend to Banach $L^0$-modules several technical tools of independent interest, such as quotient operators, summable families, and Schauder bases.