Banach空间上的强混合算子  

Strongly Mixing Operators on Banach Space

作　　者：姚玉武[1] 史恩慧[1] 周友成[1] 

机构地区：[1]苏州大学数学科学学院,江苏苏州215006

出　　处：《数学年刊（A辑）》2006年第2期189-196,共8页Chinese Annals of Mathematics

摘　　要：1999年,L．B．Gonzalez 证明了任意无限维可分 Banach 空间上存在拓扑传递的有界线性算子．这个结果肯定地回答了 S．Rolewicz 提出的问题．本文证明了由 L．B．Gonzalez 所给出的算子实际上是强混合的,同时,对加权移位算子的混合性利用权序列进行了刻划并指出任意无限维可分 Hilbert 空间上存在弱混合而非强混合的有界线性算子．In 1999, L.Bernal-Gonzalez showed that there exists a topologically transitive bounded operator on any infinite-dimensional separable Banach space. This result affirmatively solves S.Rolewicz＇s problem. This paper shows the operator given by L.Bernal-Gonzalez is in fact strongly mixing, and also characterize strongly mixing weighted shifts in terms of their weight sequence and show that any infinite-dimensional separable Hilbert space supports a weakly mixing but not strongly mixing operator.

关 键 词：拓扑传递性 弱混合 强混合 加权移位算予 BANACH空间 

分 类 号：O177.2[理学—数学]