Banach代数中理想概念的推广  

The extension of an ideal of the Banach algebra

作　　者：邓生华[1] 

机构地区：[1]中山学院基础部,中山528403

出　　处：《西南师范大学学报（自然科学版）》1999年第6期623-627,共5页Journal of Southwest China Normal University(Natural Science Edition)

摘　　要：推广了Banach代数中的理想概念．定义了半理想证明了：设B为有单位元e的Banach代数，L为B的左（右）理想，则L的Riesz扩张Lr是B的半理想.且，其中{L}为B的极大左、右理想全体．Q为B的广义幂零元全体。The definition of semi-ideal in the Banach algebra B is given. And the theroy is proved that: Ret B is a Banach algebra, which has unit elemet and if L is a left or righ ideal of B, then the Riesz extension L, of L is a semi-ideal of B, and, Where {L} is the totality of maximal left or right ideal of B. Q is the totality of the generalized nilpoenit elment of B. The Gelfond-Mazur representaion theory of the commutative Banch algebra is extended parthy.

关 键 词：极大理想 半理想 Riesz扩张 巴拿赫代数 理想 

分 类 号：O177.5[理学—数学]