Commutativity in a synaptic algebra
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David J. Foulis
und
Sylvia Pulmannová
Abstract
A synaptic algebra is a generalization of the self-adjoint part of a von Neumann algebra. For a synaptic algebra we study two weakened versions of commutativity, namely quasi-commutativity and operator commutativity, and we give natural conditions on the synaptic algebra so that each of these conditions is equivalent to commutativity. We also investigate the structure of a commutative synaptic algebra, prove that a synaptic algebra is commutative if and only if it is a vector lattice, and provide a functional representation for a commutative synaptic algebra.
Dedicated to Dr. Anatolij Dvurečenskij on the occasion of his sixty-fifth birthday (Communicated by Gejza Wimmer)
The second author was supported by Research and Development Support Agency under the contract No. APVV-0178-11 and grant VEGA 2/0059/12.
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© 2016 Mathematical Institute Slovak Academy of Sciences
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Artikel in diesem Heft
- Research Article
- Holistic logical arguments in quantum computation
- Research Article
- States with values in the Łukasiewicz groupoid
- Research Article
- On realization of effect algebras
- Research Article
- States on symmetric logics: extensions
- Research Article
- Extensions and measurability in quantum measure spaces
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- Convex subalgebras of upper bounded GMV-algebras
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- Combining boolean algebras and ℓ-groups in the variety generated by chang’s mv-algebra
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- Large rigid sets of algebras with respect to embeddability
- Research Article
- Conformal algebras, vertex algebras, and the logic of locality
- Research Article
- Extension of measures on pseudo-D-lattices
- Research Article
- Note on a parameter switching method for nonlinear ODEs
- Research Article
- Compatibility for probabilistic theories
- Research Article
- Completeness of Gelfand-Neumark-Segal inner product space on Jordan algebras
- Research Article
- Commutativity in a synaptic algebra
- Research Article
- Discrete averaged mixing applied to the logarithmic distributions
- Research Article
- Automorphisms of decompositions
