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
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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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
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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
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