Author(s): Chang Sen Yang;
Pages: 1369-1378
Year: 2008 Issue:  8
Journal: Acta Mathematica Sinica
Keyword:  *;Aluthge transformation ; Aluthge transformation ; polar decomposition ; binormal operators ; centered operators ;
Abstract: Let T = U|T| be the polar decomposition of a bounded linear operator T on a Hilbert space. The transformation is called the Aluthge transformation and means the n-th Aluthge transformation. Similarly, the transformation is called the *-Aluthge transformation and means the n-th *-Aluthge transformation. In this paper, firstly, we show that is the polar decomposition of , where is the polar decomposition. Secondly, we show that if and only if T is binormal, i.e.,..., where [A,B] = AB..BA for any operator A and B. Lastly, we show that is binormal for all non-negative integer n if and only if T is centered, and so on.