λ-Aluthge transforms and Schatten ideals Original Research Article

Let image, and let T = UmidTmid = midT*midU be the polar decomposition of T. Then, for every λ set membership, variant [0, 1] the λ-Aluthge transform is defined by Δλ(T) = midTmidλUmidTmid1-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 set membership, variant (0, 1). Moreover, we get several results which are new, even for the usual Aluthge transform.