实Banach^＊代数的Jordan^＊同态

Jordan^＊ Homomorphism of Real Banach^＊ Algebras

讨论实Banach*代数的Jordan同态.在预备中,给出引理的证明,通过引入理想、同态、半单射的定义,借用引理的证明方法和分类讨论的方法,对文中的定理予以证明并得出相应的结论.结果表明映射到*-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.

The Jordan^＊ Homomorphism of real Banach^＊ algebras is discussed. In the introduction, I have proved the lemma. By the definitions of ideal, homomorphism, semi-simple, one proved the theorem. And a set of conclusions is obtained. The results are that Jordan^＊ homomorphism of semi-simple onto real Banach^＊ algebras is continue,, the kernel is a closed^＊ ideal, and if ^＊semi-simple onto real Banach^＊ algebras is commutative, then the factor algebra is also commutative.