The Liouville−von Neumann equation and a useful decomposition of the resolvent of the generator of the time evolution operators are obtained in the formulation of quantum statistics by means of the pair of Banach spaces (τc, B), where τc is the space of the ’’trace−class’’ operators and B is the space of all bounded operators, defined on a Hilbert space.
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We make use of the following statement: let T be a closable and invertible operator defined in a Banach space χ. exists iff In the proof of the statement δ, we have used also the fact that
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One must pay attention not to mistake that is the closure of as operator defined in for that is the closure of as operator defined in
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© 1975 American Institute of Physics.
1975
American Institute of Physics
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