Abstract:

A necessary and sufficient condition for the generalized shift operator
T = Sk − (a(1)
1 , a(1)
2 , · · ·)
 e1 − · · · − (a(j)
1 , a(j)
2 , · · ·)
 ej (j  k)
on l1 to be power bounded is obtained. Moreover,this note points out that the power
bounded operator T = S − (1, 1, · · ·)
 e1 can shift a basis of [ej+1 − ej ]1
j=1,and this basis
is not equivalent to {Tne1}1
n=0.

Key words: Generalized shift operator, power bounded operator