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Article

Equicontinuity, Expansivity, and Shadowing for Linear Operators

by 1 and 2,*
1
Department of Mathematics, Chungnam National University, Daejeon 305-764, Korea
2
Nstituto de Matemática Universidade Federal do Rio de Janeiro, P. O. Box 68530, Rio de Janeiro 21945-970, Brazil
*
Author to whom correspondence should be addressed.
Axioms 2018, 7(4), 84; https://doi.org/10.3390/axioms7040084
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)
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
MDPI and ACS Style

Lee, K.; Morales, C.A. Equicontinuity, Expansivity, and Shadowing for Linear Operators. Axioms 2018, 7, 84. https://doi.org/10.3390/axioms7040084

AMA Style

Lee K, Morales CA. Equicontinuity, Expansivity, and Shadowing for Linear Operators. Axioms. 2018; 7(4):84. https://doi.org/10.3390/axioms7040084

Chicago/Turabian Style

Lee, Keonhee, and C. A. Morales. 2018. "Equicontinuity, Expansivity, and Shadowing for Linear Operators" Axioms 7, no. 4: 84. https://doi.org/10.3390/axioms7040084

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