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The Commutant of an Abstract Backward Shift

Published online by Cambridge University Press:  20 November 2018

Bruce A. Barnes
Bruce A. Barnes*
Affiliation:
Department of Mathematics University of Oregon Eugene, OR 97403 USA, email: barnes@math.uoregon.edu
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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.

Keywords

47A99backward shiftcommutant
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 43 , Issue 1 , 01 March 2000 , pp. 21 - 24
Copyright
Copyright © Canadian Mathematical Society 2000

References

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