On the boundedness of one recurrent sequence in a banach space

  • O. V. Vyatchaninov
  • M. F. Gorodnii


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 $D(A)$.
How to Cite
Vyatchaninov, O. V., and M. F. Gorodnii. “On the Boundedness of One Recurrent Sequence in a Banach Space”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, no. 9, Sept. 2009, pp. 1293-6, https://umj.imath.kiev.ua/index.php/umj/article/view/3100.
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