We consider general bounded derivations on the Banach algebra of Hilbert-Schmidt operators on an underlying complex infinite dimensional separable Hilbert space H. Their structure is described by means of unique infinite matrices. Certain classes of derivations are identified together in such a way that they correspond to a unique matrix derivation. In particular, Hadamard derivations, the action of general derivations on Hilbert-Schmidt and nuclear operators and questions about innerness are considered.
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