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Star Order and Topologies on von Neumann Algebras

  • Martin Bohata
Article

Abstract

The goal of this paper is to study a topology generated by the star order on von Neumann algebras. In particular, it is proved that the order topology under investigation is finer than \(\sigma \)-strong* topology. On the other hand, we show that it is comparable with the norm topology if and only if the von Neumann algebra is finite-dimensional.

Mathematics Subject Classification

46L10 06F30 06A06 

Notes

Acknowledgements

This work was supported by the “Grant Agency of the Czech Republic” Grant number 17-00941S, “Topological and geometrical properties of Banach spaces and operator algebras II”.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Electrical EngineeringCzech Technical University in PraguePrague 6Czech Republic

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