The order topology for a von Neumann algebra

• Autorzy: Emmanuel Chetcuti , Jan Hamhalter , Hans Weber
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 06F30: Topological lattices, order topologies
• 46L10: General theory of von Neumann algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 230
• Numer: 2
• Strony: 95-120

Daty

wydano

2015

Twórcy

autor

Emmanuel Chetcuti

• Department of Mathematics, Faculty of Science, University of Malta, Msida, Malta

autor

Jan Hamhalter

• Faculty of Electrical Engineering, Czech Technical University in Prague, Technicka 2, 166 27, Praha 6, Czech Republic

autor

Hans Weber

• Dipartimento di matematica e informatica, Università degli Studi di Udine, 1-33100 Udine, Italy

Identyfikatory

DOI

10.4064/sm8041-1-2016