广义Aluthge与广义~*-Aluthge变换的一些性质

Some properties of the generalized Aluthge and ~*-Aluthge transform

设T是作用在希耳伯特空间H上的有界线性算子,如果T=U|T|是算子T的极分解,对t∈(0,1),则T^t=|T|t|U |T|1-t和Tt(*)=|T*t|U|T*|1-t分别称为算子T的广义Aluthge变换与广义*-Aluthge变换,以此给出它们的一些性质.

Let T be a bounded linear operator on a Hilbert space H,if T = V ｜ T ｜ is a polar decomposition of T, the generalized Aluthge transform and the generalized -Aluthge transform are defined by T^~t=｜T｜t^V ｜T｜1-t^ and T^~t（＊）=｜T^＊｜t^U｜T^＊｜^1-t for t ∈（0,1）, respectively. In this note, we will give their some properties.