Preservers of λ-Aluthge transforms

Given two complex Hilbert spaces H and K with dim(H)≥2, we also show that every bijection Φ:B(H)→B(K) satisfyingΦ(Δλ(ab⁎))=Δλ(Φ(a)Φ(b)⁎), for all a,b∈B(H), must be a complex linear or a conjugate linear ⁎-isomorphism.