Effect algebras of positive linear operators densely defined on Hilbert spaces

DOI10.1016/S0034-4877(12)60009-3zbMath1250.81015OpenAlexW2013804349MaRDI QIDQ442062

Zdenka Riečanová, Sylvia Pulmannová, Michał Zając

Publication date: 9 August 2012

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0034-4877(12)60009-3

zbMATH Keywords

stateeffect algebrageneralized effect algebraoperator effect algebraordering set of statespositive linear Hilbert space operators

Mathematics Subject Classification ID

Linear operators on Banach algebras (47B48) Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) (81P10) Quantum state spaces, operational and probabilistic concepts (81P16)

Related Items (17)

Dimension theory for generalized effect algebras. ⋮ Topological properties of operator generalized effect algebras ⋮ On realization of partially ordered abelian groups ⋮ On bilinear forms from the point of view of generalized effect algebras ⋮ Hull determination and type decomposition for a generalized effect algebra ⋮ Intervals in generalized effect algebras ⋮ Hilbert space effect-representations of effect algebras ⋮ On realization of generalized effect algebras ⋮ Regular Gleason measures and generalized effect algebras ⋮ A Hilbert space operator representation of abelian po-groups of bilinear forms ⋮ The exocenter of a generalized effect algebra ⋮ Generalized effect algebras of bounded positive operators defined on Hilbert spaces ⋮ The center of a generalized effect algebra. ⋮ Generalized effect algebras of positive self-adjoint linear operators on Hilbert spaces ⋮ Blocks in pairwise summable generalized effect algebras ⋮ Representation of concrete logics and concrete generalized orthomodular posets ⋮ Top element problem and MacNeille completions of generalized effect algebras

Cites Work

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• Generalized effect algebras of positive operators densely defined on Hilbert spaces
• Effect algebras and unsharp quantum logics.
• Hilbert space operators in quantum physics
• Convex effect algebras, state ordered effect algebras, and ordered linear spaces
• Convex and linear effect algebras
• AN AXIOMATIZATION FOR ABELIAN RELATIVE INVERSES
• Proper effect algebras admitting no states

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