Nuclear Toeplitz operators between Fock spaces

Abstract

We characterize the nuclearity of Toeplitz operators $T_{\hat{I}}¼:F_{\hat{I}}{\pm }^p\to F_{\hat{I}}{\pm }^q$ with Borel measure symbols for $1\le p,q\le \infty$. For positive measures $\hat{I}¼$ and $q\le p$, we provide necessary and sufficient conditions in terms of the Berezin transform and establish a rigidity property for nuclearity across this range. In the case $p<q$, we obtain separate necessary and sufficient conditions, indicating that the Berezin transform alone is insufficient for a complete characterization. Our results extend to Fock spaces on ${\mathbb{C}}^n$.

18 pages