Lagoda O. The boundedness of solutions to linear difference equations in a Banach space

. The criteria of boundedness of solutions to linear one-parameter difference equations infinite orders with bounded operator coefficients on set of integer nonnegative numbers with initial conditions and without them in Banach space are proved. Necessary and sufficient conditions of existence and uniqueness of bounded solutions to linear one-parameter difference equation on Z without initial conditions, linear two-parameter difference equation on with initial conditions and to Rosser's system without initial condi-tions in Banach space with periodic operator coefficients are obtained. The criteria of boundedness of solutions to linear two-parameter difference equations with infinite num-ber of bounded operator coefficients are given.