1. CMB 2000 (vol 43 pp. 21)
|The Commutant of an Abstract Backward Shift |
A bounded linear operator $T$ on a Banach space $X$ is an abstract backward shift if the nullspace of $T$ is one dimensional, and the union 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 abstract backward shift is an integral domain. This result is used to derive properties of operators in the commutant.
Keywords:backward shift, commutant