论文标题
光谱订单单位空间和JB-Elgebras
Spectral order unit spaces and JB-algebras
论文作者
论文摘要
研究了订单单位空间具有可比性和光谱属性的属性。我们为具有可比性属性和光谱订单单位空间的Borel功能分积分定义了订单单位空间的连续功能演算。应用Alfsen和Schultz的条件，我们表征具有JB-Elgebras的可比性属性的订单单位空间。我们还证明了Rickart JB-Algebras的特征是每个最大关联子代数为单调$σ$ complete的JB-Elgebras，扩展了Saitô和Wright的类似结果，而Wright则用于C*-Algebras。
Order unit spaces with comparability and spectrality properties as introduced by Foulis are studied. We define continuous functional calculus for order unit spaces with the comparability property and Borel functional calculus for spectral order unit spaces. Applying the conditions of Alfsen and Schultz, we characterize order unit spaces with comparability property that are JB-algebras. We also prove a characterization of Rickart JB-algebras as those JB-algebras for which every maximal associative subalgebra is monotone $σ$-complete, extending an analogous result of Saitô and Wright for C*-algebras.
