On the asymptotic behavior of certain infinite-dimensional recurrence sequences - Tomilov, Yu. V. (Ukrains’kyi Matematychnyi Zhurnal, 1995)
Under certain conditions imposed on an operator B, we obtain criteria of boundedness of sequences x_n+1 = A x_n + Bb_n, n > 0, for any x_0 and bounded {b_n, n ≥ 0} in infinite-dimensional spaces. The results are given in terms of spectral properties of the operator A.