局部交换子及其酉系统中的r-重游荡算子

Local commutant and wandering r-tuple of operators for unitary systems

根据完全游荡向量的相关理论,引入酉系统中的r-重完全游荡算子以及局部交换子的概念。并给出局部交换子的若干性质。同时,借助局部交换子得到酉系统的全体r-重完全游荡算子的一个刻画及其他代数性质。最后,举例说明了主要结果。

According to the theory of completely wandering vector,the concepts of complete wandering operators with multiplicity r for unitary systems and local commutant are introduced.Then the properties of local commutant are given.Meanwhile,a characterization and other algebraic properties of the set of r-tuple complete wandering operators for unitary systems are obtained by means of the local commutators.Finally,some examples are given to illustrate the main results.