The iterates of an operator and their limit are studied in ergodic theory, approximation theory and other related fields. In this paper we continue the study of iterates of certain Markov operators acting on C[0,1]. We provide new sufficient conditions under which a Markov operator L is uniquely ergodic, i.e., it admits a unique invariant probability measure \(\nu \). The determination of \(\nu \) is reduced to solving an algebraic system of linear equations. Then \(\nu \) is used in order to express the limit of the iterates of L. Another useful tool in this study is the eigenstructure of L. The general results are applied to several families of classical Markov operators.

在遍历理论，逼近理论和其他相关领域中研究了算子的迭代及其极限。在本文中，我们继续研究某些作用于C [0,1]的Markov算子的迭代。我们提供了一个新的充分条件，在该条件下，马尔可夫算子L是唯一遍历遍历的，即，它接受了唯一不变性概率测度\（\ nu \）。\（\ nu \）的确定被简化为求解线性方程组的代数系统。然后使用\（\ nu \）来表示L的迭代次数的极限。这项研究中另一个有用的工具是L的本征结构。一般结果适用于几个经典马尔可夫算子族。