Operators with a strictly cyclic vector

Barnes, Bruce

doi:10.1090/S0002-9939-1973-0344924-6

Operators with a strictly cyclic vector
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by Bruce Barnes

Proc. Amer. Math. Soc. 41 (1973), 480-486

DOI: https://doi.org/10.1090/S0002-9939-1973-0344924-6

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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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