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Iterated Aluthge Transforms: A Brief Survey, Jorge Antezana, Enrique R. Pujals, Demetrio Stojanoff
Iterated Aluthge Transforms: A Brief Survey, Jorge Antezana, Enrique R. Pujals, Demetrio Stojanoff
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Given an r × r complex matrix T, if T = U|T| is the polar decomposition of T, then the Aluthge transform is defined by
∆(T) = |T|1/2U|T|1/2.
Let ∆n(T) denote the n-times iterated Aluthge transform of T, i.e. ∆0(T) = T and ∆n(T) = ∆(∆n−1(T)), n ∈ N. In this paper we make a brief survey on the known properties and applications of …