理想的Rieaz扩张的构成  

The Lonstruction of the Riesz Extension of a Ideal

作　　者：邓生华[1] 

机构地区：[1]中山学院,广东中山528402

出　　处：《西南师范大学学报（自然科学版）》2002年第4期465-467,共3页Journal of Southwest China Normal University(Natural Science Edition)

摘　　要：设B为有单位元e的Banach代数且‖e‖ =1,A为B的闭理想 .定义了A的Riesz扩张R并证明了(1)R是B的半理想 ;(2 )R =∩L∈ {L}L ALr,其中 {L}为B的极大左 ,右理想全体 ,Lr 为L的Riesz扩张 ;(3)A +Q =(A +∩L∈ {L}L ALr)∩R 。Let B is a Banach algbra with a unite e such that ‖e‖ =1. The Riesz extension R of a closed ideal A in the B was elefined, and the theory was proved that (1) R is a semi ideal of B . (2) R=∩ L∈{L} LAL r , where { L } is the totality of the maximal left or right ideal of B , L\-r is the Riesz extension of L . (3) A+Q=(A+∩ L∈{L} LAL\-r)∩R, where Q is the tolality of generalized nipotent of B .

关 键 词：BANACH代数 闭理想 Riesz扩张 半理想 广义幂零元 RIESZ算子 极大理想 

分 类 号：O177.5[理学—数学]