On the universal sl_2 invariant of ribbon bottom tangles

A bottom tangle is a tangle in a cube consisting of arc components whose boundary points are on a line in the bottom square of the
cube. A ribbon bottom tangle is a bottom tangle whose closure is a ribbon link.
For every $n$-component ribbon bottom tangle $T$, we prove that the universal invariant of $T$ associated to the quantized enveloping algebra $U_h(sl_2)$ is contained in a certain subalgebra of the $n$-fold completed tensor power of $U_h(sl_2)$. This result is applied to the colored Jones polynomial of ribbon links.