lambda-Aluthge transforms and Schatten ideals

J. ANTEZANA, P. MASSEY Y D. STOJANOFF

LINEAR ALGEBRA AND ITS APPLICATIONS

Birkhauser

Año: 2005 vol. 405 p. 177 - 199

0024-3795

Let $T \in L(H)$, and let $T=U|T|=|T^*|U$ be the polar decomposition of $T$. Then, for every $\lambda \in [0,1]$,  the $\lambda$-Aluthge transform is defined by $\Delta_\lambda (T )= |T|^{\lambda } U |T |^{1-\lambda}$.  We show that several properties which are known for the usual Aluthge transform (i.e. the case $\lambda = 1/2$) also hold for $\lambda$-Aluthge transforms with $lambda \in (0,1)$. Moreover, we get several results which are new, even for the usual Aluthge transform.