具有连续对合运算的实Banach*代数的Jordan结构

On Jordan Structure of Real Banach* Algebras with Continuous Involution

本文讨论了实Banach*代数的Jordan结构．主要结果:第一部分指出映射到 *-半单实Banach*代数上的Jordan*同态是连续的,且其核空间是闭*理想;由映射到交换实Banach*代数上的Jordan*同态诱导的因子代数也是交换的．第二部分介绍了两个不同的锥,并讨论了他们间的关系．另外,我们得到了关于实Banach*代数*- 根基的一个新的刻画．本文是Satish Shirali的工作的实化．

In this paper, the Jordan structure of real Banach＊ algebras is discussed. In part one, the results are that the continuity of a Jordan. homomorphism T of A1 onto A2, where A2 is＊ semi-simple, is automatic, the kernel is a closed ＊ ideal ,and if A2 is commutative, then the factor algebra A1/ker （T） is also commutative. In part two, two different cones of a real Banach＊ algebra are introduced, and their relation is studied. Moreover, we obtain a new characterization of the .＊-radical of a real Banach＊ algebra. This paper is thereal counterpart of Satish Shirali＇s work in the complex case.