λ-Aluthge transforms and schatten ideals

Abstract

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