  In this paper, we consider Rota-Baxter operators on involutive associative
algebras. We define cohomology for Rota-Baxter operators on involutive algebras
that governs the formal deformation of the operator. This cohomology can be
seen as the Hochschild cohomology of a certain involutive associative algebra
with coefficients in a suitable involutive bimodule. We also relate this
cohomology with the cohomology of involutive dendriform algebras. Finally, we
show that the standard Fard-Guo construction of the functor from the category
of dendriform algebras to the category of Rota-Baxter algebras restricts to the
involutive case.
