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Sur le spectre des opérateurs rigides

Part of: Topological dynamics General theory of linear operators

Published online by Cambridge University Press:  01 March 2022

PIERRE MAZET  and
ERIC SAIAS
PIERRE MAZET
Affiliation:
Independent Scholar (e-mail: piermazet@laposte.net)
ERIC SAIAS*
Affiliation:
Sorbonne Université, Laboratoire de Probabilités, Statistique et Modélisation (LPSM) 4, place Jussieu, 75252 Paris Cedex 05, France
*
e-mail: eric.saias@upmc.fr
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Abstract

For any $r\in [0,1]$ we give an example of a rigid operator whose spectrum is the annulus $\{\lambda\in \mathbb{C} : r \le |\lambda| \le 1 \} $. In particular, when $r=0$ this operator is rigid and non-invertible, and when $r\in {\kern1pt}] 0,1 [ $ this operator is invertible but its inverse is not rigid. This answers two questions of Costakis, Manoussos and Parissis [Recurrent linear operators. Complex Anal. Oper. Theory 8 (2014), 1601–1643].

Keywords

dynamical systemsrigid operatorsspectrum47A10

MSC classification

Primary: 37B20: Notions of recurrence 47A10: Spectrum, resolvent

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 43 , Issue 4 , April 2023 , pp. 1351 - 1362
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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Footnotes

Pour Mustapha Krazem, à l’occasion de son soixantiéme anniversaire

References

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