Continuity of the map $S \to \left| S \right|$ for linear operators

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.

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