Geodesic
On normal derivations of Hilbert–Schmidt type
Glasgow mathematical journal, Tome 29 (1987) no. 2, pp. 245-248

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Let H denote a separable, infinite dimensional Hilbert space. Let B(H), C2 and C1 denote the algebra of all bounded linear operators acting on H, the Hilbert–Schmidt class and the trace class in B(H) respectively. It is well known that C2 and C1 each form a two-sided-ideal in B(H) and C2 is itself a Hilbert space with the inner productwhere {ei} is any orthonormal basis of H and tr(.) is the natural trace on C1. The Hilbert–Schmidt norm of X ∈ C2 is given by IIXII2=(X, X)1⁄2. 
Kittaneh, Fuad. On normal derivations of Hilbert–Schmidt type. Glasgow mathematical journal, Tome 29 (1987) no. 2, pp. 245-248. doi: 10.1017/S0017089500006893
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