Schatten properties, nuclearity and minimality of shift invariant spaces

Abstract

We extend Feichtinger's minimality property on smallest non-trivial time-frequency shift invariant Banach spaces, to the quasi-Banach case. Analogous properties are deduced for certain matrix classes. We use these results to prove that $\mathrm{Op}(a)$ is a Schatten-$q$ operator from $M^{\infty }$ to $M^p$ and $r$-nuclear operator from $M^{\infty }$ to $M^r$ when $a\in M^r$ for suitable $p$, $q$ and $r$ in $(0,\infty ]$.

Now 26 pages. Previous title: "Minimality of time-frequency shift invariant spaces and Schatten properties for quasi-Banach spaces". It now contain results on minimality of matrix classes. Versions 1 and 2 contained mistakes about Schatten results which are corrected. A section on p-nuclear operators is added

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