The order topology for a von Neumann algebra

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F15%3A00240873" target="_blank" >RIV/68407700:21230/15:00240873 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.4064/sm8041-1-2016" target="_blank" >http://dx.doi.org/10.4064/sm8041-1-2016</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4064/sm8041-1-2016" target="_blank" >10.4064/sm8041-1-2016</a>

Result language
angličtina
Original language name
The order topology for a von Neumann algebra
Original language description
The order topology tau(o)(P) (resp. the sequential order topology tau(os)(P)) on a poset P is the topology that has as its closed sets those that contain the order limits of all their order convergent nets (resp. sequences). For a von Neumann algebra M we consider the following three posets: the self-adjoint part M-sa, the self-adjoint part of the unit ball M-sa(1), and the projection lattice P(M). We study the order topology (and the corresponding sequential variant) on these posets, compare the ordertopology to the other standard locally convex topologies on M, and relate the properties of the order topology to the underlying operator-algebraic structure of M.
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
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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
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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