论文标题
投影 - 无用的Rickart Jordan结构
A projection--less approach to Rickart Jordan structures
论文作者
论文摘要
本文的主要目的是介绍和探索一个弱Rickart JB $^*$ - 三倍的概念。我们介绍了弱订单的Rickart JB $^*$ - 三倍，我们表明c $^*$ - 代数$ a $是弱（订单）Rickart JB $^*$ - 当它是弱Rickart C $^*$的三重精确度时。我们还证明，在弱序的Rickart JB $^*$中，与三重动力相关的Peirce-2子空间 - 从Ayupov和Arzikulov的意义上讲，Triple是Rickart JB $^*$ - 代数。通过扩展Rickart C $^*$ - 代数的古典属性，我们证明每个弱订购的Rickart JB $^*$ - 三重订单都是由其三重态生成的。
The main goal of this paper is to introduce and explore an appropriate notion of weakly Rickart JB$^*$-triples. We introduce weakly order Rickart JB$^*$-triples, and we show that a C$^*$-algebra $A$ is a weakly (order) Rickart JB$^*$-triple precisely when it is a weakly Rickart C$^*$-algebra. We also prove that the Peirce-2 subspace associated with a tripotent in a weakly order Rickart JB$^*$-triple is a Rickart JB$^*$-algebra in the sense of Ayupov and Arzikulov. By extending a classical property of Rickart C$^*$-algebras, we prove that every weakly order Rickart JB$^*$-triple is generated by its tripotents.
