Local spectral theory and orbits of operators

Miller, T.; Miller, V.

doi:10.1090/S0002-9939-99-04639-0

Local spectral theory and orbits of operators
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by T. L. Miller and V. G. Miller PDF

Proc. Amer. Math. Soc. 127 (1999), 1029-1037 Request permission

Abstract:

For $T\in \mathcal {L}(X)$, we give a condition that suffices for $\varphi (T)$ to be hypercyclic where $\varphi$ is a nonconstant function that is analytic on the spectrum of $T$. In the other direction, it is shown that a property introduced by E. Bishop restricts supercyclic phenomena: if $T\in \mathcal {L}(X)$ is finitely supercyclic and has Bishop’s property $(\beta )$, then the spectrum of $T$ is contained in a circle.

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