Absolutely Summing Toeplitz operators on Fock spaces

Abstract

For $1\le p<\infty$, let $F_{\ddot{I}}^p†$ be the Fock spaces on ${\mathbb{C}}^n$ with the weight function $\ddot{I}†$ that \(φ\in {\mathcal{C}}^{2}\left( {\mathbb{C}}^{n}\right)\) is real-valued and satisfies $m{\ddot{I}‰}_0\le d{d}^c\ddot{I}†\le M{\ddot{I}‰}_0$ for two positive constants \(m\) and \(M\), \({ω}_{0} = d{d}^{c}{\left| z\right| }^{2}\) is the Euclidean Kähler form on \({\mathbb{C}}^{n}\), \({d}^{c} = \frac{\sqrt{-1}}{4}\left( {\bar{\partial } - \partial }\right)\). In this paper, we completely characterize those positive Borel measure $\hat{I}¼$ on ${\mathbb{C}}^n$ so that the induced Toeplitz operators $T_{\hat{I}}¼$ is $r$-summing on $F_{\ddot{I}}{†}^p$ for $r\ge 1$.