The iterated Aluthge transforms of a 2-by-2 matrix converge

By T. Andô, T. Yamazaki. 2003

50 citations recorded by the source corpus.

Abstract The Aluthge transform of a square complex matrix T with polar representation T=U|T| is by definition Δ (T)≡|T| 1 2 U|T| 1 2 . It has been conjectured that the iterates Δ(T),Δ(Δ(T)),… converge. We prove this when T is a 2-by-2 matrix.

Subfields: Algebra and Number Theory, Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/9797ccf9843804aee25bb533925a38bb03312fee

Citations in the corpus

• Aluthge Transforms of Complex Symmetric Operators (2008, unknown): “This transformation arose in the study of hyponormal operators [1] and has since been studied in many different contexts [3, 4, 5, 6, 8, 9, 10, 32].”