The Commutant of an Abstract Backward Shift

Canadian mathematical bulletin

关键词: backward shift;    commutant;   

DOI  :  10.4153/CMB-2000-003-9

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

A bounded linear operator $T$ on a Banach space $X$ is an abstractbackward shift if the nullspace of $T$ is one dimensional, and theunion of the null spaces of $T^k$ for all $k geq 1$ is dense in$X$. In this paper it is shown that the commutant of an abstractbackward shift is an integral domain. This result is used toderive properties of operators in the commutant.

【 授权许可】

Unknown