A projection and an effect in a synaptic algebra
Functional Analysis
2016-05-24 v2
Abstract
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, applieas on this settinh, and we introduce and study two candidates for a commutator for p and e.
Keywords
Cite
@article{arxiv.1507.08965,
title = {A projection and an effect in a synaptic algebra},
author = {David J. Foulis and Anna Jencova and Sylvia Pulmannova},
journal= {arXiv preprint arXiv:1507.08965},
year = {2016}
}
Comments
24 pages, comments welcome