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Affiliated subspaces and the structure 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%3A00206061" target="_blank" >RIV/68407700:21230/13:00206061 - isvavai.cz</a>

  • Result on the web

    <a href="http://dx.doi.org/10.7900/jot.2010jul07.1894" target="_blank" >http://dx.doi.org/10.7900/jot.2010jul07.1894</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.7900/jot.2010jul07.1894" target="_blank" >10.7900/jot.2010jul07.1894</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Affiliated subspaces and the structure of von neumann algebras

  • Original language description

    The interplay between order-theoretic properties of structures of subspaces affiliated with a von Neumann algebra M and the inner structure of the algebra M is studied. The following characterization of finiteness is given: a von Neumann algebra M is finite if and only if in each representation space of M one has that closed affiliated subspaces are given precisely by strongly closed left ideals in M. Moreover, it is shown that if the modular operator of a faithful normal state ? is bounded, then all important classes of affiliated subspaces in the GNS representation space of ? coincide. Orthogonally closed affiliated subspaces are characterized in terms of the supports of normal func-tionals. It is proved that complete affiliated subspaces correspondto left ideals generated by finite sums of orthogonal atomic projections

  • 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

    Journal of Operator Theory

  • ISSN

    0379-4024

  • e-ISSN

  • Volume of the periodical

    69

  • Issue of the periodical within the volume

    1

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    15

  • Pages from-to

    101-115

  • UT code for WoS article

    000319784400006

  • EID of the result in the Scopus database