Geodesic
The Commutant of an Abstract Backward Shift
Canadian mathematical bulletin, Tome 43 (2000) no. 1, pp. 21-24

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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.
DOI : 10.4153/CMB-2000-003-9
Mots-clés : 47A99, backward shift, commutant 
Barnes, Bruce A. The Commutant of an Abstract Backward Shift. Canadian mathematical bulletin, Tome 43 (2000) no. 1, pp. 21-24. doi: 10.4153/CMB-2000-003-9
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