On weakly unitarily invariant norm and the λ-Aluthge transformation for invertible operator

Let be an invertible operator with polar decomposition T = UP and commute with T. In this paper we prove that PλBUP1−λ BT , where • is a weakly unitarily invariant norm on and 0 λ 1. As the consequence of this result, we have f(PλUP1−λ) f(T) for any polynomial f.