Only ‘free’ measures are admissable on 𝐹(𝑆) when the inner product space 𝑆 is incomplete

DOI10.1090/S0002-9939-07-08982-4zbMath1138.46014MaRDI QIDQ5438462

David Buhagiar, Emmanuel Chetcuti

Publication date: 23 January 2008

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

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Characterizations of Hilbert spaces (46C15) States of selfadjoint operator algebras (46L30)

Related Items (7)

Affiliated subspaces and infiniteness of von Neumann algebras ⋮ Order topology on orthocomplemented posets of linear subspaces of a pre-Hilbert space ⋮ Subspace structures in inner product spaces and von Neumann algebras ⋮ Classes of invariant subspaces for some operator algebras ⋮ Probability structures in subspace lattice approach to foundations of quantum theory ⋮ On Gleason's theorem without Gleason ⋮ Quasi-splitting subspaces and Foulis-Randall subspaces

Cites Work

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• A finitely additive state criterion for the completeness of inner product spaces
• A Completeness Criterion for Inner Product Spaces
• Correction to: "Inner Product Spaces"
• THE STATE-SPACE OF THE LATTICE OF ORTHOGONALLY CLOSED SUBSPACES
• A remark on Piron's paper
• Quantum measure theory

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