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• # Artykuł - szczegóły

## Studia Mathematica

2015 | 230 | 2 | 95-120

## The order topology for a von Neumann algebra

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.

95-120

wydano
2015

### Twórcy

autor
• Department of Mathematics, Faculty of Science, University of Malta, Msida, Malta
autor
• Faculty of Electrical Engineering, Czech Technical University in Prague, Technicka 2, 166 27, Praha 6, Czech Republic
autor
• Dipartimento di matematica e informatica, Università degli Studi di Udine, 1-33100 Udine, Italy