Nuclear Weighted composition operators between different $L^p$-spaces

TL;DR

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

Contribution

It provides a complete characterization of nuclear weighted composition operators between distinct L^p spaces, highlighting the triviality on non-atomic measure spaces.

Findings

Nuclear weighted composition operators are fully characterized between L^p spaces.

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

The results clarify the structure of nuclear operators in this setting.

Abstract

We provide complete characterisations of nuclear weighted composition operators between two distinct $L^p(\mu)$-spaces, where $1\leq p<\infty$. As a consequence, when the underlying measure space is non-atomic, the only nuclear weighted composition operator between $L^p(\mu)$-spaces is the zero operator.