A formula for the numerical range of an elementary operator on C*-algebra

Let $\text{A}$ be a $C^{\ast }-$algebra with unit element $1$ and unitary group $U\mathrm{.}$ Let $a=(a_1,\mathrm{.}\mathrm{.}\mathrm{.},a_k)$ and $b=(b_1,\mathrm{.}\mathrm{.}\mathrm{.},b_k)$ two $k-$tuples of elements in $\text{A}\mathrm{.}$ The elementary operator associated to $a$ and $b$ is defined by $ R_{a, b} (x)= \sum_{i=1}^ {k} a_ixb_i.$ In this paper we prove the following formula for the numerical range of $R_{a,b}$: $$V(R_{a,b},B(\text{A}))=[\cup \{V(\sum _{i=1}^k{u}^{\ast }{a}_{i}u{b}_i,\text{A}):u\in U\}{]}^{-}\mathrm{.}$$ This formulat solves the problem 4.5 of \cite{Fi}.