The iterated Aluthge transforms of a matrix converge
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- 作者：Jorge Antezana ; Enrique R. Pujals ; Demetrio Stojanoff
- 关键词：Aluthge transform ; Stable manifold theorem ; Similarity orbit ; Polar decomposition
- 刊名：Advances in Mathematics
- 出版年：2011
- 出版时间：30 January 2011
- 年：2011
- 卷：226
- 期：2
- 页码：1591-1620
- 全文大小：352 K
文摘
Given an r×r complex matrix T, if T=UT is the polar decomposition of T, then, the Aluthge transform is defined byΔ(T)=T1/2UT1/2. Let Δn(T) denote the n-times iterated Aluthge transform of T, i.e., Δ0(T)=T and Δn(T)=Δ(Δn−1(T)), . We prove that the sequence converges for every r×r matrix T. This result was conjectured by Jung, Ko and Pearcy in 2003. We also analyze the regularity of the limit function.