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The Commutant of an Abstract Backward Shift
Published online by Cambridge University Press: 20 November 2018
Abstract
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
$k\,\ge \,1$ 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.
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- Copyright © Canadian Mathematical Society 2000
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