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An expression of spectral radius via Aluthge transformation

Authors:	Takeaki Yamazaki

Institution:	Department of Mathematics, Kanagawa University, Yokohama 221-8686, Japan

Abstract:	For an operator $T\in B(H)$ , the Aluthge transformation of is defined by $\widetilde{T}=\vert T\vert^{\frac{1}{2}}U\vert T\vert^{\frac{1}{2}}$ . And also for a natural number , the -th Aluthge transformation of is defined by $\widetilde{T_{n}}=\widetilde{(\widetilde{T_{n-1}})}$ and $\widetilde{T_{1}}=\widetilde{T}$ . In this paper, we shall show $\begin{displaymath}\lim_{n\to \infty}\Vert\widetilde{T_{n}}\Vert=r(T),\end{displaymath}$ where is the spectral radius.

Keywords:	Aluthge transformation Heinz inequality spectral radius

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