  We discuss Toeplitz operators on the Segal-Bargmann space as functional
realizations of anti-Wick operators on the Fock space. In the special case of
radial symbols we exploit the isometric mapping between the Segal-Bargmann
space and $l^2$ complex sequences in order to establish conditions such that an
equivalence between Toeplitz operators and diagonal operators on $l^2$ holds.
We also analyze the inverse problem of mapping diagonal operators on $l^2$ into
Toeplitz form. The composition problem of Toeplitz operators with radial
symbols is reviewed as an application. Our notation and basic examples make
contact with Quantum Mechanics literature.
