Weighted conditional expectation operators and nuclearity

Abstract

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

12 pages