The order topology on duals of C*-algebras and 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%2F20%3A00346256" target="_blank" >RIV/68407700:21230/20:00346256 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4064/sm190108-11-7" target="_blank" >https://doi.org/10.4064/sm190108-11-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4064/sm190108-11-7" target="_blank" >10.4064/sm190108-11-7</a>
Alternative languages
Result language
angličtina
Original language name
The order topology on duals of C*-algebras and von Neumann algebras
Original language description
For a von Neumann algebra M, we study the order topology associated to the hermitian part M-*(s), and to intervals of the predual M-*. It is shown that the order topology on M-*(s) coincides with the topology induced by the norm. In contrast, it is proved that the condition of having the order topology, associated to the interval [0, phi], equal to the topology induced by the norm, for every phi is an element of M-*(+), is necessary and sufficient for the commutativity of M. It is also proved that if phi is a positive bounded functional on a C*-algebra A, then the norm-null sequences in [0, phi] coincide with the null sequences, with respect to the order topology on [0, phi], if and only if the von Neumann algebra pi(phi)(A)' is of finite type (where pi(phi) denotes the corresponding GNS representation). This fact allows us to give a new topological characterization of finite von Neumann algebras. Moreover, we demonstrate that convergence to zero for norm and order topology, on order-bounded parts of dual spaces, are inequivalent for all C*-algebras that are not of type I.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Studia Mathematica
ISSN
0039-3223
e-ISSN
1730-6337
Volume of the periodical
254
Issue of the periodical within the volume
3
Country of publishing house
PL - POLAND
Number of pages
18
Pages from-to
219-236
UT code for WoS article
000558107800001
EID of the result in the Scopus database
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