On the asymptotic behavior of certain infinite-dimensional recurrence sequences

Abstract

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 $A$.