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Affilated subspaces and infiniteness of von Neumann algebras

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F13%3A00206174" target="_blank" >RIV/68407700:21230/13:00206174 - isvavai.cz</a>

  • Result on the web

    <a href="http://dx.doi.org/10.1002/mana.201200157" target="_blank" >http://dx.doi.org/10.1002/mana.201200157</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1002/mana.201200157" target="_blank" >10.1002/mana.201200157</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Affilated subspaces and infiniteness of von Neumann algebras

  • Original language description

    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.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

    <a href="/en/project/GAP201%2F12%2F0290" target="_blank" >GAP201/12/0290: Topological and geometrical properties of Banach spaces and operator algebras</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Others

  • Publication year

    2013

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Mathematische Nachrichten

  • ISSN

    0025-584X

  • e-ISSN

  • Volume of the periodical

    286

  • Issue of the periodical within the volume

    10

  • Country of publishing house

    DE - GERMANY

  • Number of pages

    10

  • Pages from-to

    976-985

  • UT code for WoS article

    000325856300006

  • EID of the result in the Scopus database