Best $n$-term approximation of diagonal operators and application to function spaces with mixed smoothness

In this paper we give exact values of the best $n$-term approximation widths of diagonal operators between $\ell_p(\mathbb{N})$ and $\ell_q(\mathbb{N})$ with $0<p,q\leq \infty$. The result will be applied to obtain the asymptotic constants of best $n$-term approximation widths of embeddings of function spaces with mixed smoothness by trigonometric system.