The order topology on the projection lattice of a Hilbert space

DOI10.1016/J.TOPOL.2011.03.018zbMath1257.06013OpenAlexW2039463303MaRDI QIDQ429314

Hans Weber, David Buhagiar, Emmanuel Chetcuti

Publication date: 19 June 2012

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2011.03.018

zbMATH Keywords

Hilbert spacestrong operator topologyorder topologynorm topology

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Ordered topological structures (06F30) Connections of general topology with other structures, applications (54H99)

Related Items (7)

Order topology on orthocomplemented posets of linear subspaces of a pre-Hilbert space ⋮ Kernel maps and operator decomposition ⋮ Preservation of order and orthogonality on preduals of Jordan algebras ⋮ The order topology on duals of $C^\ast $-algebras and von Neumann algebras ⋮ The order topology for a von Neumann algebra ⋮ Star order and topologies on von Neumann algebras ⋮ On different modes of order convergence and some applications

Cites Work

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• Matrix methods in analysis
• Orthomodular structures as quantum logics. Transl. from the Slovak
• The Weak Convergence of Unit Vectors to Zero in Hilbert Space is the Convergence of One-Dimensional Subspaces in the Order Topology
• The Interval Topology of a Lattice
• A Characterization of Reflexivity by the Lattice of Closed Subspaces
• Quantum measure theory

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