摘要
A necessary and sufficient condition for the generalized shift operator T = S-k - (a(1)((1)), a(2)((1)),...) x e(1) - ... -(a(1)((j)), a(2)((j)),...) x e(j) (j greater than or equal to k) on l(1) to be power bounded is obtained. Moreover,this note points out that the power bounded operator T = S - (1, 1,...) x c(1) can shift a basis of [e(j+1) - e(j)](j = 1)(infinity), and this basis is not equivalent to {T(n)e(1)} (infinity)(n=0).
A necessary and sufficient condition for the generalized shift operator T = S-k - (a(1)((1)), a(2)((1)),...) x e(1) - ... -(a(1)((j)), a(2)((j)),...) x e(j) (j greater than or equal to k) on l(1) to be power bounded is obtained. Moreover,this note points out that the power bounded operator T = S - (1, 1,...) x c(1) can shift a basis of [e(j+1) - e(j)](j = 1)(infinity), and this basis is not equivalent to {T(n)e(1)} (infinity)(n=0).
基金
the Education DepartmentFoundation of Henan province.
