Generalized n-idempotents and Hyper-generalized n-idempotents  

作　　者：邓春源 李启慧 杜鸿科 

机构地区：[1]College of Mathematics and Information Science,Shaanxi Normal University,Xi'an,710062 School of Mathematics Science,South China Normal University,Guangzhou,510631 [2]College of Mathematics and Information Science,Shaanxi Normal University,Xi'an,710062

出　　处：《Northeastern Mathematical Journal》2006年第4期387-394,共8页东北数学（英文版）

基　　金：The NNSF(10571113)of Shaanxi Province,Chins.

摘　　要：For an integer n ≥2, we say that an operator A is an n-idempotent if A^n = A; A is a generalized n-idempotent if A^n = A^＊; A is a hyper-generalized n. idempotent if A^n = A^＋. The set of all n-idempotents, all generalized n-idempotents and all hyper-generalized n-idempotents are denoted by In（H）, gIn（H） and HgIn（H）, respectively. In this note, we obtain a chain of proper inclusions gIn（H） belong to HgIn（H） belong to In＋2（H）.For an integer n ≥2, we say that an operator A is an n-idempotent if A^n = A; A is a generalized n-idempotent if A^n = A^＊; A is a hyper-generalized n. idempotent if A^n = A^＋. The set of all n-idempotents, all generalized n-idempotents and all hyper-generalized n-idempotents are denoted by In（H）, gIn（H） and HgIn（H）, respectively. In this note, we obtain a chain of proper inclusions gIn（H） belong to HgIn（H） belong to In＋2（H）.

关 键 词：IDEMPOTENT generalized inverse normal operator 

分 类 号：O177.6[理学—数学]