The iterated Aluthge transforms of a matrix converge

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dc.creatorAntezana, Jorge
dc.creatorPujals, Enrique R.
dc.creatorStojanoff, Demetrio
dc.date2007-11-23
dc.date.accessioned2026-07-07T08:44:40Z
dc.date.available2026-07-07T08:44:40Z
dc.descriptionGiven an $r\times r$ complex matrix $T$, if $T=U|T|$ is the polar decomposition of $T$, then, the Aluthge transform is defined by $$ Δ(T)= |T|^{1/2} U |T |^{1/2}. $$ Let $Δ^{n}(T)$ denote the n-times iterated Aluthge transform of $T$, i.e. $Δ^{0}(T)=T$ and $Δ^{n}(T)=Δ(Δ^{n-1}(T))$, $n\in\mathbb{N}$. We prove that the sequence $\{Δ^{n}(T)\}_{n\in\mathbb{N}}$ 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.
dc.description23 pages
dc.identifierhttps://arxiv.org/abs/0711.3727
dc.identifierhttp://arxiv.org/abs/0711.3727
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/142741
dc.subjectFunctional Analysis
dc.subjectDynamical Systems
dc.subject37D10; 15A60
dc.titleThe iterated Aluthge transforms of a matrix converge
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