The iterated Aluthge transforms of a matrix converge

作者：Antezana Jorge^*; Pujals Enrique R; Stojanoff Demetrio

来源：Advances in Mathematics, 2011, 226(2): 1591-1620.

DOI：10.1016/j.aim.2010.08.012

• Aluthge transform
• Stable manifold theorem
• Similarity orbit
• Polar decomposition

Given an r x r complex matrix T, if T = U vertical bar T vertical bar is the polar decomposition of T, then, the Aluthge transform is defined by
Delta(T) = vertical bar T vertical bar(1/2)U vertical bar T vertical bar(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 is an element of N. We prove that the sequence {Delta(n)(T)}(n is an element of N) converges for every r x r matrix T. This result was conjectured by Jung, Ko and Pearcy in 2003. We also analyze the regularity of the limit function.

• 出版日期2011-1-30