Lattice properties of subspace families in an inner product space

DOI10.1090/S0002-9939-01-05855-5zbMath0968.03077MaRDI QIDQ2718979

Hans Weber, Pavel Pták

Publication date: 14 May 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

latticeHilbert spacecompletenessorthomodular posetstateinner product spacesplitting subspace

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Complemented lattices, orthocomplemented lattices and posets (06C15) Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) (81P10) Quantum logic (03G12)

Related Items (13)

Orthosystems of submodules of a module ⋮ Orthomodular lattices that are \(Z_2\)-rich ⋮ Sequential convergence of regular measures on prehilbert space logics ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On complete-cocomplete subspaces of an inner product space. ⋮ Recent progress on pre-Hilbert-space logics and their measure spaces ⋮ Pre-Hilbert spaces with anomalous splitting and orthogonally-closed subspace structures ⋮ Order topology on orthocomplemented posets of linear subspaces of a pre-Hilbert space ⋮ Subspace structures in inner product spaces and von Neumann algebras ⋮ Orthonormal bases and quasi-splitting subspaces in pre-Hilbert spaces ⋮ Boundedness of nonadditive quantum measures ⋮ Quantum logics that are symmetric-difference-closed

Cites Work

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• Ein nicht-klassischer Hilbertscher Raum
• State on splitting subspaces and completeness of inner product spaces
• Orthomodular lattices whose MacNeille completions are not orthomodular
• On the definition of Hilbert space
• Some characterizations of the underlying division ring of a Hilbert lattice by automorphisms
• A Completeness Criterion for Inner Product Spaces
• Characterization of hilbert spaces by orthomodular spaces
• Orthomodularity in infinite dimensions; a theorem of M. Solèr
• Decompositions in Quantum Logic
• A remark on Piron's paper

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