Synaptic algebras

Mathematica Slovaca

David Foulis¹ 

关键词: spectral order-unit normed space;    special Jordan algebra;    convex effect algebra;    orthomodular lattice;    generalized Hermitian algebra;    convex effect algebra;    projections;    square roots;    carriers;    absolute value;    polar decoposition;    quadratic mapping;    Sasaki mapping;    invertible element;    regular element;    simple element;    spectral resolution;    spectrum;   

DOI  :  10.2478/s12175-010-0037-3

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

A synaptic algebra is both a special Jordan algebra and a spectral order-unit normed space satisfying certain natural conditions suggested by the partially ordered Jordan algebra of bounded Hermitian operators on a Hilbert space. The adjective “synaptic”, borrowed from biology, is meant to suggest that such an algebra coherently “ties together” the notions of a Jordan algebra, a spectral order-unit normed space, a convex effect algebra, and an orthomodular lattice.

【 授权许可】

Unknown