Continuity of the map $S \to \left| S \right|$ for linear operators
Tosio Kato · Proceedings of the Japan Academy Series A Mathematical Sciences · 1973
H, H') to B(H) given by [S1=(S*S)1/2; here B(H,H') denotes the set o all bounded linear operators on a Hilbert space H to another Hilbert space H', and B(H) the set of all bounded seladjoint operators in H.We shall prove the ollowing results.