Resumen de Convergence of the iterated Aluthge transform sequence for diagonalizable matrices

Jorge Abel Antezana, Enrique R. Pujals, Demetrio Stojanoff

• Abstract 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)), . We prove that the sequence converges for every r×r diagonalizable matrix T. We show that the limit ?8() is a map of class C8 on the similarity orbit of a diagonalizable matrix, and on the (open and dense) set of r×r matrices with r different eigenvalues.