Nuclear weighted conditional expectation operators

TL;DR

This paper characterizes nuclear weighted conditional expectation operators between different L^p spaces and shows that, on non-atomic measure spaces, the only such nuclear operator is the zero operator.

Contribution

It provides a complete characterization of nuclear weighted conditional expectation operators and establishes that the zero operator is the only nuclear one on non-atomic measure spaces.

Findings

Characterization of nuclear weighted conditional expectation operators.

On non-atomic spaces, only the zero operator is nuclear.

Provides conditions for nuclearity in L^p spaces.

Abstract

We provide a characterisations of nuclear weighted conditional expectation operators between different $L^p(\mu)$-spaces. As a consequence, when the underlying measure space is non-atomic, the only nuclear weighted conditional expectation operator between different $L^p(\mu)$-spaces is the zero operator.