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Spaces of operators with bounded projector trace. (Ukrainian. English summary) Zbl 1199.81047

Summary: In many scientific works devoted to the investigation of quantum many-particle systems, evolution is described by a group of operators acting in the space \({\mathcal L}^1 (\mathcal{H})\) of operators with bounded trace over a Hilbert space \(\mathcal{H}\). But this space does not fit for the investigation of problems which have a natural examination in the class of operators with translation-invariant kernels, because these operators do not belong to the space \({\mathcal L}^1 (\mathcal{H})\). This paper is devoted to the construction and investigation of more general operator spaces.

MSC:

81V70 Many-body theory; quantum Hall effect
82D15 Statistical mechanics of liquids
47D06 One-parameter semigroups and linear evolution equations
81R15 Operator algebra methods applied to problems in quantum theory
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