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The Commutant of an Abstract Backward Shift

Open Access article
 Printed: Mar 2000
  • Bruce A. Barnes
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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 backward shift, commutant
MSC Classifications: 47A99 show english descriptions None of the above, but in this section 47A99 - None of the above, but in this section

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