Denote by T the bounded linear operator on a complex Hilbert space X and let T = U|T | be any polar decomposition of T with U a partial isometry and |T | = (T ∗T ) 1 2 . Then, the Aluthge transform Te of T is the operator ...

The Aluthge transform Te of a bounded linear operator T on a complex Hilbert space X is the operator |T| 1 2 U|T| 1 2 . Here, T = U|T| is any polar decomposition of T with U a partial isometry and |T| = (T ∗T) 1 2 . This ...