λ-Aluthge transforms and Schatten ideals

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 Δλ(T) = ∣T∣λU∣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.