非游荡性及Kato意义下的逼近

Nonwandering property and approximation in sense of Kato

在略掉无条件基的情形下,以构造的方式,研究了l1上单边(加权)后移位算子并推广了Salas的一个结果,使得它们在适当的条件下可构成非游荡算子;同时,从微分动力学中拓扑共轭的角度出发,证明了当Banach空间序列{Xn}≥1在Kato意义下逼近Banach空间X时,空间序列上的有界线性算子Tn,T的非游荡性在一定的条件可以相互保持,并得到几个相应的结果;进而为非游荡算子扰动问题的研究提供了一条思路.

In the case of omitting unconditional basis, and by using a constructive technique, the nonwandering unilateral weighted backward shifts on l^1 is studied when general shifts satisfy some extra hypothesis. Simultaneously, if let ｛T_n｝_(n≥1)be a bounded linear operator sequence on Banach space X_n converging in the sense of Kato to a bounded operator T on the Banach space X, then by generalizing topologic conjugate property in the infinite dimensional Banach space,the nonwandering property of ｛T_n｝_(n≥1) can be inherited by T under the appropriate conditions. Several consequences are also obtained. Thus, it provides an approach to study the perturbation of nonwandering operators.