Regular elements in generalized hermitian algebras

Mathematica Slovaca

David Foulis¹  Sylvia Pulmannová¹ 

关键词: GH-algebra;    effect;    projection;    orthomodular lattice;    order-unit space;    carrier projection;    comparability property;    square root;    absolute value;    spectral resolution;    spectrum;    regular element;    C-block;   

DOI  :  10.2478/s12175-011-0002-9

学科分类：数学（综合）

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

【 摘 要 】

A generalized Hermitian (GH) algebra is a special Jordan algebra that is at the same time a spectral order-unit space. In this paper we characterize the von Neumann regular elements in a GH-algebra, relate maximal pairwise commuting subsets of the algebra to blocks in its projection lattice, and prove a Gelfand-Naimark type representation theorem for commutative GH-algebras.

【 授权许可】

Unknown