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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An expression of spectral radius via Aluthge transformation


Author: Takeaki Yamazaki
Journal: Proc. Amer. Math. Soc. 130 (2002), 1131-1137
MSC (2000): Primary 47A13, 47A30.
Published electronically: September 19, 2001
MathSciNet review: 1873788
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Abstract: 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

\begin{displaymath}\lim_{n\to \infty}\Vert\widetilde{T_{n}}\Vert=r(T),\end{displaymath}

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


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Additional Information

Takeaki Yamazaki
Affiliation: Department of Mathematics, Kanagawa University, Yokohama 221-8686, Japan
Email: yamazt26@kanagawa-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06283-9
PII: S 0002-9939(01)06283-9
Keywords: Aluthge transformation, Heinz inequality, spectral radius.
Received by editor(s): October 27, 2000
Published electronically: September 19, 2001
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2001 American Mathematical Society