English

Absolutely Summing Toeplitz operators on Fock spaces

Functional Analysis 2025-09-25 v1 Complex Variables

Abstract

For 1p<1\le p<\infty, let FφpF^p_\varphi be the Fock spaces on Cn{\mathbb C}^n with the weight function φ\varphi that φC2(Cn)\varphi \in {\mathcal{C}}^{2}\left( {\mathbb{C}}^{n}\right) is real-valued and satisfies mω0ddcφMω0 m{\omega }_{0} \leq d{d}^{c}\varphi \leq M{\omega }_{0} for two positive constants mm and MM, ω0=ddcz2{\omega }_{0} = d{d}^{c}{\left| z\right| }^{2} is the Euclidean K\"{a}hler form on Cn{\mathbb{C}}^{n}, dc=14(ˉ){d}^{c} = \frac{\sqrt{-1}}{4}\left( {\bar{\partial } - \partial }\right). In this paper, we completely characterize those positive Borel measure μ\mu on Cn{\mathbb C}^n so that the induced Toeplitz operators TμT_\mu is rr-summing on FφpF_{\varphi}^{p} for r1r \ge 1.

Keywords

Cite

@article{arxiv.2509.19967,
  title  = {Absolutely Summing Toeplitz operators on Fock spaces},
  author = {Zhangjian Hu and Ermin Wang},
  journal= {arXiv preprint arXiv:2509.19967},
  year   = {2025}
}
R2 v1 2026-07-01T05:53:54.143Z