A projection and an effect in a synaptic algebra

作者：Foulis David J; Jencova Anna; Pulmannova Sylvia^*

来源：Linear Algebra and Its Applications, 2015, 485: 417-441.

DOI：10.1016/j.laa.2015.07.039

• Synaptic algebra
• Projection
• Effect
• Peirce decomposition
• Commutator
• CBS-decomposition

We study a pair p, e consisting of a projection p (an idempotent) and an effect e (an element between 0 and 1) in a synaptic algebra (a generalization of the self-adjoint part of a von Neumann algebra). We show that some of Halmos's theory of two projections (or two subspaces), including a version of his CS-decomposition theorem, applies in this setting, and we introduce and study two candidates for a commutator projection for p and e.

• 出版日期2015-11-15