Completeness of inner product spaces with respect to splitting subspaces

DOI10.1007/BF00417459zbMath0601.46026OpenAlexW2058223728MaRDI QIDQ1081077

Gianpiero Cattaneo, Giuseppe Marino

Publication date: 1986

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00417459

zbMATH Keywords

inner product spaceannihilationsplitting subspaces\(\sigma \)-latticeorthocomplemented complete latticeorthoposet

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)

Related Items (11)

Gleason's theorem and completeness criteria ⋮ Completeness of inner product spaces and quantum logic of splitting subspaces ⋮ Alcuni interessanti posets di sottospazi di uno spazio pre-Hilbert ⋮ Recent progress on pre-Hilbert-space logics and their measure spaces ⋮ State on splitting subspaces and completeness of inner product spaces ⋮ Pre-Hilbert spaces with anomalous splitting and orthogonally-closed subspace structures ⋮ States on families of subspaces of pre-Hilbert spaces ⋮ Bibliography on quantum logics and related structures ⋮ Quantum logics and completeness criteria of inner product spaces ⋮ Orthogonality spaces and atomistic orthocomplemented lattices ⋮ Quasi-splitting subspaces and Foulis-Randall subspaces

Cites Work

• On the definition of Hilbert space
• Orthomodular posets from sesquilinear forms
• Correction to: "Inner Product Spaces"
• Inner Product Spaces

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