Table of Contents
Journal of Operators
Volume 2014 (2014), Article ID 196345, 6 pages
http://dx.doi.org/10.1155/2014/196345
Research Article

Discrete -Dichotomy and Remarks on the Boundedness of the Projections

1Department of Mathematics, Faculty of Mathematics and Computer Science, West University of Timișoara, 4 Parvan Boulevard, 300223 Timișoara, Romania
2Academy of Romanian Scientists, 54 Independenţei Street, 050094 Bucharest, Romania

Received 18 November 2013; Revised 29 May 2014; Accepted 9 June 2014; Published 6 July 2014

Academic Editor: Jan Lang

Copyright © 2014 Mihai-Gabriel Babuţia et al. 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

The present paper treats a concept of -dichotomy for linear discrete systems. Sufficient conditions for the -boundedness of the projection sequences that give the dichotomy are presented and an illustrative example shows the connection between the growth of the system and the bound of the sequence of projections. Thus the growth of the system that is assumed in the theorems is essential.