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The Commutant of an Abstract Backward Shift

Published online by Cambridge University Press:  20 November 2018

Bruce A. Barnes*
Affiliation:
Department of Mathematics University of Oregon Eugene, OR 97403 USA, email: [email protected]
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Abstract

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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 $k\,\ge \,1$ 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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2000

References

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