2017
Том 69
№ 6

All Issues

On the boundedness of one recurrent sequence in a banach space

Gorodnii M. F., Vyatchaninov O. V.

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Abstract

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 $D(A)$.

English version (Springer): Ukrainian Mathematical Journal 61 (2009), no. 9, pp 1529-1532.

Citation Example: Gorodnii M. F., Vyatchaninov O. V. On the boundedness of one recurrent sequence in a banach space // Ukr. Mat. Zh. - 2009. - 61, № 9. - pp. 1293-1296.

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