Algebraic properties of Toeplitz operators on generalized Fock spaces on ${\mathbb{C}}^d$

Abstract

We study two problems involving algebraic properties of Toeplitz operators on generalized Fock spaces on ${\mathbb{C}}^d$ with weights of the form ${\left|z\right|}^{2s}{e}^{-{|z|}^{2m}}$, $m\ge 1,s\ge 0$. We determine the commutant of a given Toeplitz operator with a radial symbol which satisfies certain growth conditions. We also discuss the equation $T_f{T}_g=0$, when $f$ or $g$ is radial.

References in corpus (1)

• The commutants of certain Toeplitz operators on weighted Bergman spaces