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

 

Operators with a strictly cyclic vector


Author: Bruce Barnes
Journal: Proc. Amer. Math. Soc. 41 (1973), 480-486
MSC: Primary 47A65
MathSciNet review: 0344924
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Abstract: In this paper, operators that have a strictly cyclic vector in a Banach space $ X$ are studied. It is shown that the spectrum of such operators has some special properties. When $ X$ is a Hilbert space, the connection between having a strictly cyclic vector and irreducibility is explored. If $ X$ is an infinite dimensional Hilbert space, it is shown that no hyponormal operator on $ X$ has a strictly cyclic vector.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0344924-6
PII: S 0002-9939(1973)0344924-6
Keywords: Strictly cyclic vector, strictly cyclic operator
Article copyright: © Copyright 1973 American Mathematical Society