This is an announcement for the paper "Carl's inequality for quasi-Banach spaces" by Aicke Hinrichs, Anton Kolleck, and Jan Vybiral. Abstract: We prove that for any two quasi-Banach spaces $X$ and $Y$ and any $\alpha>0$ there exists a constant $c_\alpha>0$ such that $$ \sup_{1\le k\le n}k^{\alpha}e_k(T)\le c_\alpha \sup_{1\le k\le n} k^\alpha c_k(T) $$ holds for all linear and bounded operators $T:X\to Y$. Here $e_k(T)$ is the $k$-th entropy number of $T$ and $c_k(T)$ is the $k$-th Gelfand number of $T$. For Banach spaces $X$ and $Y$ this inequality is widely used and well-known as Carl's inequality. For general quasi-Banach spaces it is a new result, which closes a gap in the argument of Donoho in his seminal paper on compressed sensing. Archive classification: math.FA Remarks: 12 pages Submitted from: aicke.hinrichs@jku.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1512.04421 or http://arXiv.org/abs/1512.04421