Local spectral theory and orbits of operators
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- by T. L. Miller and V. G. Miller PDF
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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.References
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Additional Information
- T. L. Miller
- Affiliation: Department of Mathematics, Mississippi State University, Drawer MA, Mississippi State, Mississippi 39762
- Email: miller@math.msstate.edu
- V. G. Miller
- Affiliation: Department of Mathematics, Mississippi State University, Drawer MA, Mississippi State, Mississippi 39762
- Email: vivien@math.msstate.edu
- Received by editor(s): December 23, 1996
- Received by editor(s) in revised form: July 11, 1997
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 1029-1037
- MSC (1991): Primary 47B40, 47B99
- DOI: https://doi.org/10.1090/S0002-9939-99-04639-0
- MathSciNet review: 1473674