Normality properties of Volterra-type integral operators on the Fock space

We investigate several normality-type properties of bounded Volterra-type integral operators Vg V g acting on the Fock space. We show that this class contains no nonzero normal or quasinormal operators, and that Vg V g is binormal if and only if either the quadratic or the linear term in the polynomial representation of the symbol g vanishes. We further prove that the properties of being normaloid, subnormal, hyponormal, paranormal, totally paranormal, p -hyponormal, $$*$$ ∗ -paranormal, and quasi- $$*$$ ∗ -paranormal are all equivalent and are characterized by the absence of the linear term in g . These results reveal a clear distinction between the roles of the linear and quadratic terms in determining the normality behavior of these operators. Finally, we show that every bounded Volterra-type integral operator on the Fock space is essentially normal.