Convergence of iterated Aluthge transform sequence for diagonalizable matrices II: $λ$-Aluthge transform

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dc.creatorAntezana, Jorge
dc.creatorPujals, Enrique
dc.creatorStojanoff, Demetrio
dc.date2007-06-08
dc.date.accessioned2026-07-07T08:04:41Z
dc.date.available2026-07-07T08:04:41Z
dc.descriptionLet $λ\in (0,1)$ and let $T$ be a $r\times r$ complex matrix with polar decomposition $T=U|T|$. Then, the $\la$- Aluthge transform is defined by $$ Δ_λ(T )= |T|^λ U |T |^{1-λ}. $$ Let $Δ_λ^{n}(T)$ denote the n-times iterated Aluthge transform of $T$, $n\in\mathbb{N}$. We prove that the sequence $\{Δ_λ^{n}(T)\}_{n\in\mathbb{N}}$ converges for every $r\times r$ {\bf diagonalizable} matrix $T$. We show regularity results for the two parameter map $(\la, T) \mapsto \alulit{\infty}{T}$, and we study for which matrices the map $(0,1)\ni λ\mapsto Δ_λ^{\infty}(T)$ is constant.
dc.description24 pages
dc.identifierhttps://arxiv.org/abs/0706.1234
dc.identifierhttp://arxiv.org/abs/0706.1234
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130057
dc.subjectFunctional Analysis
dc.subject37D10; 15A60
dc.titleConvergence of iterated Aluthge transform sequence for diagonalizable matrices II: $λ$-Aluthge transform
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