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Affiliated subspaces and infiniteness of von Neumann algebras

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dc.contributor.author Hamhalter J.
dc.contributor.author Turilova E.
dc.date.accessioned 2018-09-18T20:06:15Z
dc.date.available 2018-09-18T20:06:15Z
dc.date.issued 2013
dc.identifier.issn 0025-584X
dc.identifier.uri https://dspace.kpfu.ru/xmlui/handle/net/136537
dc.description.abstract We show that the structural properties of von Neumann algebra s are connected with the metric and order theoretic properties of various classes of affiliated subspaces. Among others we show that properly infinite von Neumann algebra s always admit an affiliated subspace for which (1) closed and orthogonally closed affiliated subspaces are different; (2) splitting and quasi-splitting affiliated subspaces do not coincide. We provide an involved construction showing that concepts of splitting and quasi-splitting subspaces are non-equivalent in any GNS representation space arising from a faithful normal state on a Type I factor. We are putting together the theory of quasi-splitting subspaces developed for inner product spaces on one side and the modular theory of von Neumann algebra s on the other side. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
dc.relation.ispartofseries Mathematische Nachrichten
dc.subject GNS representation
dc.subject Quasi-splitting subspaces
dc.subject Subspaces affiliated with a von Neuman algebra
dc.subject Subspaces in pre-Hilbert spaces
dc.title Affiliated subspaces and infiniteness of von Neumann algebras
dc.type Article
dc.relation.ispartofseries-issue 10
dc.relation.ispartofseries-volume 286
dc.collection Публикации сотрудников КФУ
dc.relation.startpage 976
dc.source.id SCOPUS0025584X-2013-286-10-SID84879712924


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  • Публикации сотрудников КФУ Scopus [24551]
    Коллекция содержит публикации сотрудников Казанского федерального (до 2010 года Казанского государственного) университета, проиндексированные в БД Scopus, начиная с 1970г.

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