Liouville space is itself a Hilbert space under the Hilbert-Schmidt inner product.
[1][2] Abstractly, Liouville space is equivalent (isometrically isomorphic) to the tensor product of a Hilbert space with its dual.
[1][3] A common computational technique to organize computations in Liouville space is vectorization.
[2] Liouville space underlies the density operator formalism and is a common computation technique in the study of open quantum systems.
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