Grushka, Yaroslav Spaces of operators with bounded projector trace. (Ukrainian. English summary) Zbl 1199.81047 Mat. Visn. Nauk. Tov. Im. Shevchenka 6, 73-86 (2009). 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. Cited in 1 Document 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 Keywords:quantum many-particle system; operators with translation-invariant kernels PDFBibTeX XMLCite \textit{Y. Grushka}, Mat. Visn. Nauk. Tov. Im. Shevchenka 6, 73--86 (2009; Zbl 1199.81047)