Products of Toeplitz operators on the Fock space

Hon Rae Cho; Jong-Do Park; Kehe Zhu

Products of Toeplitz operators on the Fock space

Functional Analysis 2012-12-04 v1 Complex Variables

Authors: Hon Rae Cho , Jong-Do Park , Kehe Zhu

Abstract

Let $f$ and $g$ be functions, not identically zero, in the Fock space $F^2$ of $C_n$ . We show that the product $T_fT_{\bar g}$ of Toeplitz operators on $F^2$ is bounded if and only if $f(z)=e^{q(z)}$ and $g(z)=ce^{-q(z)}$ , where $c$ is a nonzero constant and $q$ is a linear polynomial.

Keywords

Toeplitz operators Fock space bounded operators product of operators linear polynomial complex analysis

Cite

@article{arxiv.1212.0045,
  title  = {Products of Toeplitz operators on the Fock space},
  author = {Hon Rae Cho and Jong-Do Park and Kehe Zhu},
  journal= {arXiv preprint arXiv:1212.0045},
  year   = {2012}
}

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