Weighted conditional expectation operators and nuclearity

TL;DR

This paper characterizes nuclear weighted conditional expectation operators on 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 on L^p spaces and establishes their triviality on non-atomic measure spaces.

Findings

Nuclear weighted conditional expectation operators are characterized explicitly.

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

The results clarify the structure of these operators in functional analysis.

Abstract

We provide a characterisations of nuclear weighted conditional expectation operators on $L^p(\mu)$-spaces, for $1\leq p<\infty$. As a consequence, when the underlying measure space is non-atomic, the only nuclear weighted conditional expectation operator on $L^p(\mu)$-spaces is the zero operator.