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
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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
Mathematische Nachrichten
ISSN
0025-584X
e-ISSN
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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
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