Affiliation:
1. Emeritus Professor Department of Mathematics and Statistics University of Massachusetts Amherst, MA Postal Address: 1 Sutton Court Amherst, MA 01002 USA
2. Mathematical Institute Slovak Academy of Sciences Štefánikova 49 SK–814 73 Bratislava SLOVAKIA
Abstract
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.
Cited by
9 articles.
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1. Observables on synaptic algebras;Fuzzy Sets and Systems;2021-02
2. Synaptic Algebras as Models for Quantum Mechanics;International Journal of Theoretical Physics;2019-02-21
3. Kadison’s antilattice theorem for a synaptic algebra;Demonstratio Mathematica;2018-01-25
4. Spectral Order on a Synaptic Algebra;Order;2018-01-16
5. Banach Synaptic Algebras;International Journal of Theoretical Physics;2017-12-14