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Hilbert-schmidt OperatorIn mathematics, a Hilbert-Schmidt operator is a bounded operator A on a Hilbert space H1->H2 such that there exists an orthonormal basis of H1 such that -
is finite. Let A and B are two Hilbert-Schmidt operators, the Hilbert-Schmidt inner product can be defined as This definition is independent of the choice of orthonormal basis The Hilbert-Schmidt operators form an ideal in the algebra of bounded operators on H, which is usually not closed in the norm topology. They also form a Hilbert space, and can be shown to be isometrically isomorphic to the tensor product of Hilbert spaces .
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