Table of Contents
ISRN Mathematical Analysis
Volume 2011 (2011), Article ID 281737, 27 pages
http://dx.doi.org/10.5402/2011/281737
Research Article

Dynamics of a Compact Operator

Department of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, VA 22030, USA

Received 22 December 2010; Accepted 13 January 2011

Academic Editor: V. Y. Glizer

Copyright © 2011 Teck-Cheong Lim. 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.

Abstract

Let 𝑇 ∢ 𝑋 β†’ 𝑋 be a compact linear (or more generally affine) operator from a Banach space into itself. For each π‘₯ ∈ 𝑋 , the sequence of iterates 𝑇 𝑛 π‘₯ , 𝑛 = 0 , 1, … and its averages βˆ‘ ( 1 / π‘˜ ) 𝑛 π‘˜ = 0 𝑇 π‘˜ βˆ’ 1 π‘₯ , 𝑛 = 0 , 1, … are either bounded or approach infinity.