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Axioms 2018, 7(4), 84; https://doi.org/10.3390/axioms7040084

Equicontinuity, Expansivity, and Shadowing for Linear Operators

1
Department of Mathematics, Chungnam National University, Daejeon 305-764, Korea
2
Nstituto de Matem√°tica Universidade Federal do Rio de Janeiro, P. O. Box 68530, Rio de Janeiro 21945-970, Brazil
*
Author to whom correspondence should be addressed.
Received: 22 September 2018 / Revised: 9 November 2018 / Accepted: 11 November 2018 / Published: 15 November 2018
(This article belongs to the Special Issue Shadowing in Dynamical Systems)
Full-Text   |   PDF [219 KB, uploaded 15 November 2018]

Abstract

We prove that a linear operator of a complex Banach space has a shadowable point if and only if it has the shadowing property. In addition, every equicontinuous linear operator does not have the shadowing property and its spectrum is contained in the unit circle. Finally, we prove that if a linear operator is expansive and has the shadowing property, then the origin is the only nonwandering point. View Full-Text
Keywords: linear operator; banach space; shadowable point; equicontinuous linear operator; banach space; shadowable point; equicontinuous
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Lee, K.; Morales, C.A. Equicontinuity, Expansivity, and Shadowing for Linear Operators. Axioms 2018, 7, 84.

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