Classes of Invariant Subspaces for Some Operator Algebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F14%3A00221712" target="_blank" >RIV/68407700:21230/14:00221712 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s10773-013-1740-y" target="_blank" >http://dx.doi.org/10.1007/s10773-013-1740-y</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10773-013-1740-y" target="_blank" >10.1007/s10773-013-1740-y</a>

Result language
angličtina
Original language name
Classes of Invariant Subspaces for Some Operator Algebras
Original language description
New results showing connections between structural properties of von Neumann algebras and order theoretic properties of structures of invariant subspaces given by them are proved. We show that for any properly infinite von Neumann algebra M there is an affiliated subspace L such that all important subspace classes living on L are different. Moreover, we show that L can be chosen such that the set of ?-additive measures on subspace classes of L are empty. We generalize measure theoretic criterion on completeness of inner product spaces to affiliated subspaces corresponding to Type I factor with finite dimensional commutant. We summarize hitherto known results in this area, discuss their importance for mathematical foundations of quantum theory, and outline perspectives of further research.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

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)

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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