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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Strictly cyclic weighted shifts


Author: Alan Lambert
Journal: Proc. Amer. Math. Soc. 29 (1971), 331-336
MSC: Primary 47.40
MathSciNet review: 0275213
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Abstract: E. Nordgren recently showed that certain weighted shift operators on Hilbert space have the property that they commute with no unbounded closed densely defined linear transformations. In the present paper, it is shown that this property for a weighted shift operator is equivalent to the existence of a strictly cyclic vector for the weakly closed algebra generated by the weighted shift. After establishing some tests for the existence of such a strictly cyclic vector, several further examples are given of weighted shift operators satisfying Nordgren's commutativity property.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0275213-4
PII: S 0002-9939(1971)0275213-4
Keywords: Weighted shift operators, closed linear transformations, strictly cyclic vectors, commutant of a weighted shift
Article copyright: © Copyright 1971 American Mathematical Society