We establish a criterion for the existence and uniqueness of solutions of a linear difference equation with an unbounded operator coefficient belonging to the space $l_p(B)$ of sequences of elements of a Banach space $B$.
Citation Example:Gorodnii M. F. $l_p$-Solutions of One Difference Equation in a Banach Space // Ukr. Mat. Zh. - 2003. - 55, № 3. - pp. 425-430.