A characterization of the class of partial isometries

Let B(H)B(H) be the set of all bounded linear operators on a Hilbert space HH. In this paper we show that if S   is a closed range operator with R(S)=R(S*)R(S)=R(S*), then‖S∗⊗S†+S†⊗Sast‖λ=2,‖S∗⊗S†+S†⊗Sast‖λ=2,if and only if S is a non-zero real scalar of a normal partial isometry. Also we find some other characterizations of this space using some inequalities related to Corach–Porta–Recht inequality.