Completeness of inner product spaces and quantum logic of splitting subspaces

DOI10.1007/BF00398592zbMath0652.46017OpenAlexW2079169496MaRDI QIDQ1107062

Anatolij Dvurečinskij

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1007/bf00398592

zbMATH Keywords

inner product spacequantum logicsplitting subspacesorthocomplemented orthomodular \(\sigma\)-orthoposed

Mathematics Subject Classification ID

Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) (81P10) Quantum logic (03G12) Inner product spaces and their generalizations, Hilbert spaces (46C99)

Related Items (17)

Gleason's theorem and completeness criteria ⋮ Decompositions of measures on orthoalgebras and difference posets ⋮ Test spaces, Dacey spaces, and completeness of inner product spaces ⋮ Noncommutative version of Nikodym boundedness theorem for uniform space- valued functions ⋮ 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 ⋮ Event structures in nonstandard quantum mechanics ⋮ States on families of subspaces of pre-Hilbert spaces ⋮ A signed measure completeness criterion ⋮ Bibliography on quantum logics and related structures ⋮ Quantum logics and completeness criteria of inner product spaces ⋮ Regular measures and inner product spaces ⋮ D-test spaces and difference posets ⋮ Orthogonality spaces and atomistic orthocomplemented lattices ⋮ Unnamed Item ⋮ Quasi-splitting subspaces and Foulis-Randall subspaces

Cites Work

• Completeness of inner product spaces with respect to splitting subspaces
• On the definition of Hilbert space
• A Completeness Criterion for Inner Product Spaces
• Probability in physics and a theorem on simultaneous observability
• Correction to: "Inner Product Spaces"
• Inner Product Spaces
• Partial Solution to Mackey's Problem about Modular Pairs and Completeness

This page was built for publication: Completeness of inner product spaces and quantum logic of splitting subspaces