Let $TA$ denote the space underlying the tensor algebra of a vector space $A$. In this short note, we show that if $A$ is a differential graded algebra, then $TA$ is a differential Batalin-Vilkovisky algebra. Moreover, if $A$ is an $A_\infty$ algebra, then $TA$ is a commutative $BV_\infty$ algebra.
Journal of Homotopy and Related Structures, Vol. 6(2011), No. 1, pp. 177-182