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

Abstract

We provide complete characterisations of nuclear weighted composition operators between two distinct $L^p(\hat{I}¼)$-spaces, where $1\le p<\infty$. As a consequence, when the underlying measure space is non-atomic, the only nuclear weighted composition operator between $L^p(\hat{I}¼)$-spaces is the zero operator.

9 pages