An expression of spectral radius via Aluthge transformation

For an operator $T\in B(H)$, the Aluthge transformation of $T$ is defined by $\widetilde{T}=\vert T\vert^{\frac{1}{2}}U\vert T\vert^{\frac{1}{2}}$. And also for a natural number $n$, the $n$-th Aluthge transformation of $T$ is defined by $\widetilde{T_{n}}=\widetilde{(\widetilde{T_{n-1}})}$ and $\widetilde{T_{1}}=\widetilde{T}$. In this paper, we shall show

where $r(T)$ is the spectral radius.