2019
Том 71
№ 9

All Issues

Vyatchaninov O. V.

Articles: 1
Brief Communications (Ukrainian)

On the boundedness of one recurrent sequence in a banach space

Gorodnii M. F., Vyatchaninov O. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2009. - 61, № 9. - pp. 1293-1296

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 $D(A)$.