  Motivated by the recent paper of Boggiatto-Garello in J. Pseudo-Differ. Oper.
Appl. \textbf{11} (2020), 93-117, where a Gabor operator is regarded as
pseudodifferential operator with symbol $p(x,\omega)$ periodic on both the
variables, we study the continuity and invertibility, on general time frequency
invariant spaces, of pseudodifferential operators with completely periodic
symbol and general $\tau$ quantization.
