# Equicontinuity, Expansivity, and Shadowing for Linear Operators

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## Abstract

**:**

## 1. Introduction

**Theorem**

**1.**

**Theorem**

**2.**

**Theorem**

**3.**

## 2. Proof of the Theorems

**Theorem**

**4.**

- 1.
- T has the shadowing property.
- 2.
- T has a shadowable point.
- 3.
- 0 is a shadowable point of T.

**Proof.**

**Lemma**

**1.**

- 1.
- T is equicontinuous.
- 2.
- T is power bounded namely ${sup}_{n\in \mathbb{Z}}\parallel {T}^{n}\parallel <\infty $ (see Reference [11]).

**Proof.**

**Corollary**

**1.**

**Lemma**

**2.**

**Proof.**

**Proof of Theorem**

**2.**

**Proof of Theorem**

**3.**

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**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