Commutativity in a synaptic algebra
| Autor: | Sylvia Pulmannová, David J. Foulis |
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| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Mathematica Slovaca. 66:469-482 |
| ISSN: | 1337-2211 0139-9918 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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