On operator-valued free convolution powers Dimitri Shlyakhtenko 46L54free probability We give an explicit realization of the $\eta$-convolution power of an $A$-valued distribution, as defined earlier by Anshelevich, Belinschi, Fevrier, and Nica. Where $\eta:A\to A$ is completely positive and $\eta\geq\operatorname{id}$, we give a short proof of positivity of the $\eta$-convolution power of a positive distribution. Conversely, where $\eta\not\geq\operatorname{id}$, and $s$ is large enough, we construct an $s$-tuple whose $A$-valued distribution is positive, but has non-positive $\eta$-convolution power. Indiana University Mathematics Journal 2013 text pdf 10.1512/iumj.2013.62.4863 10.1512/iumj.2013.62.4863 en Indiana Univ. Math. J. 62 (2013) 91 - 97 state-of-the-art mathematics http://iumj.org/access/