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Local spectral theory and orbits of operators

Authors: T. L. Miller and V. G. Miller
Journal: Proc. Amer. Math. Soc. 127 (1999), 1029-1037
MSC (1991): Primary 47B40, 47B99
MathSciNet review: 1473674
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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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Additional Information

T. L. Miller
Affiliation: Department of Mathematics, Mississippi State University, Drawer MA, Mississippi State, Mississippi 39762

V. G. Miller
Affiliation: Department of Mathematics, Mississippi State University, Drawer MA, Mississippi State, Mississippi 39762

Received by editor(s): December 23, 1996
Received by editor(s) in revised form: July 11, 1997
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1999 American Mathematical Society