The following screenshot is from J.C.Bourin and E.Y.Lee's paper"Pinchings and positive linear maps". When reading the proof of Corollary 3.6, I met with some problems.

Notation: $W_e()$ denotes the essential numerical range of an operator in $L(H)$.

How to show that $W_e\left(\begin{pmatrix}I & 0\\R_{\epsilon}& 0\end{pmatrix}\right)=W_e\left(\bigoplus\limits_{n=1}^{\infty}\begin{pmatrix}1 & 0\\a_n& 0\end{pmatrix}\right)$?

My thought: if we find a unitary operator $U\in L(H)$ such that $U\begin{pmatrix}I & 0\\R_{\epsilon}& 0\end{pmatrix}U^*=\bigoplus\limits_{n=1}^{\infty}\begin{pmatrix}1 & 0\\a_n& 0\end{pmatrix}$, then the above conclusion holds, but how to construct the uniatry operator?