Об асимптотическом поведении некоторых бесконечномерных рекуррентных последовательностей

Abstract

Under certain conditions imposed on an operator B, we obtain criteria of boundedness of sequences xn+1=Axn+Bbn,n>0, for any x0 and bounded {bn,n≥0} in infinite-dimensional spaces. The results are given in terms of spectral properties of the operator A.