Banach代数中理想概念的推广

The extension of an ideal of the Banach algebra

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.