Lambda-Aluthge transforms and Schatten Ideals

J. ANTEZANA; P. MASSEY; D. STOJANOFF

LINEAR ALGEBRA AND ITS APPLICATIONS

ELSEVIER SCIENCE INC

Lugar: Amsterdam; Año: 2005 p. 177 - 199

0024-3795

Let $T\in\op$, 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 $\Delta_\lambda \left(T \right)= |T|^{\lambda } U |T |^{1-\lambda}$. 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.