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An expression of spectral radius via Aluthge transformation

Authors:	Takeaki Yamazaki

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

Abstract:	For an operator , the Aluthge transformation of is defined by $widetilde{T}=vert Tvert^{frac{1}{2}}Uvert Tvert^{frac{1}{2}}$ . 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 $begin{displaymath}lim_{nto infty}Vertwidetilde{T_{n}}Vert=r(T),end{displaymath}$ where is the spectral radius.

Keywords:	Aluthge transformation Heinz inequality spectral radius.

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