Essential Norm of Toeplitz Operators on the Fock Spaces

Abstract

In this paper, we show that, on the generalized Fock space \({F^p(\varphi)}\) with \({1 < p < \infty}\) , the essential norm of a noncompact Toeplitz operator \({T_\mu}\) with \({|\mu|}\) being a Fock–Carleson measure equals its distance to the set of compact Toeplitz operators. Moreover, the distance is realized by infinitely many compact Toeplitz operators. Our approach is also available on the Bergman space setting.