| Let A,B are two Banach algebra with unit, if T:A→B is a continuous homormophism with unit, we give the defination of T-wely elments and T-Fredholm elments by the homormorphsim T,when the range of T is B. If (1) B is the closed two-side ideal of A , and (?)g sr (B)≤2. (2)if a∈Fred_t(A),ind(a) = 0,we get that a∈Fred_T~0(A).If T(A) is closed under inverse, KerT without order, lgsr(A)≤2,then we get Fred_T~0(A) is closed in Fred_T(A). |
