The iterated Aluthge transforms of a matrix converge

Details The iterated Aluthge transforms of a matrix converge The iterated Aluthge transforms of a matrix converge

2007-11-23

arxiv.org/abs/0711.3727v1

Mathematics

Functional Analysis

23 pages

Scientific paper

Given an $r\times r$ complex matrix $T$, if $T=U|T|$ is the polar decomposition of $T$, then, the Aluthge transform is defined by $$ \Delta(T)= |T|^{1/2} U |T |^{1/2}. $$ Let $\Delta^{n}(T)$ denote the n-times iterated Aluthge transform of $T$, i.e. $\Delta^{0}(T)=T$ and $\Delta^{n}(T)=\Delta(\Delta^{n-1}(T))$, $n\in\mathbb{N}$. We prove that the sequence $\{\Delta^{n}(T)\}_{n\in\mathbb{N}}$ converges for every $r\times r$ matrix $T$. This result was conjecturated by Jung, Ko and Pearcy in 2003. We also analyze the regularity of the limit function.

Affiliated with

Also associated with

No associations

Rating

The iterated Aluthge transforms of a matrix converge does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The iterated Aluthge transforms of a matrix converge, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The iterated Aluthge transforms of a matrix converge will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-363607