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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Noncompact commutators in the commutant of a cyclic operator


Author: James D. Stafney
Journal: Proc. Amer. Math. Soc. 106 (1989), 385-389
MSC: Primary 47B47; Secondary 47B99
DOI: https://doi.org/10.1090/S0002-9939-1989-0953012-9
MathSciNet review: 953012
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Abstract: We show that the commutant of the operator $ S \otimes \left( {I + {S^*}} \right)$, where $ S$ is the shift operator, contains two operators $ A$ and $ B$ such that $ AB - BA$ is not compact operator.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0953012-9
Keywords: Commutant, cyclic operator, commutator
Article copyright: © Copyright 1989 American Mathematical Society

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