TY - JOUR
AU - O. V. Vyatchaninov
AU - M. F. Gorodnii
PY - 2009/09/25
Y2 - 2024/05/30
TI - On the boundedness of one recurrent sequence in a banach space
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 61
IS - 9
SE - Short communications
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/3100
AB - We establish necessary and sufficient conditions under which a sequence $x_0 = y_0,\; x_{n+1} = Ax_n + y_{n+1},\; n ≥ 0$, is bounded for each bounded sequence $\{y_n : n ⩾ 0\} ⊂ \left\{x ∈ ⋃^{∞}_{n=1} D(A_n)|\sup_{n ⩾ 0} ∥A^nx∥ < ∞\right\}$, where $A$ is a closed operator in a complex Banach space with domain of definition $D(A)$.
ER -