The order topology for a von Neumann algebra

Emmanuel Chetcuti, Jan Hamhalter, and Hans Weber. "The order topology for a von Neumann algebra." Studia Mathematica 230.2 (2015): 95-120. <http://eudml.org/doc/285742>.

@article{EmmanuelChetcuti2015,
abstract = {The order topology $τ_\{o\}(P)$ (resp. the sequential order topology $τ_\{os\}(P)$) 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 $M¹_\{sa\}$, and the projection lattice P(M). We study the order topology (and the corresponding sequential variant) on these posets, compare the order topology 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.},
author = {Emmanuel Chetcuti, Jan Hamhalter, Hans Weber},
journal = {Studia Mathematica},
keywords = {von Neumann algebra; order topology; Mackey topology; mixed topology},
language = {eng},
number = {2},
pages = {95-120},
title = {The order topology for a von Neumann algebra},
url = {http://eudml.org/doc/285742},
volume = {230},
year = {2015},
}

TY - JOUR
AU - Emmanuel Chetcuti
AU - Jan Hamhalter
AU - Hans Weber
TI - The order topology for a von Neumann algebra
JO - Studia Mathematica
PY - 2015
VL - 230
IS - 2
SP - 95
EP - 120
AB - The order topology $τ_{o}(P)$ (resp. the sequential order topology $τ_{os}(P)$) 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 $M¹_{sa}$, and the projection lattice P(M). We study the order topology (and the corresponding sequential variant) on these posets, compare the order topology 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.
LA - eng
KW - von Neumann algebra; order topology; Mackey topology; mixed topology
UR - http://eudml.org/doc/285742
ER -