We extend Feichtinger's minimality property on the smallest non-trivial time-frequency shift invariant Banach space, to the quasi-Banach case. Analogous properties are deduced for certain matrix spaces.

We use these results to prove that the pseudo-differential operator Op(a) is a Schatten-q operator from M^∞ to M^p and r-nuclear operator from M^∞ to M^r when a∈M^r for suitable p, q and r in (0,∞].