Table of Contents Author Guidelines Submit a Manuscript
International Journal of Analysis
Volume 2013 (2013), Article ID 397262, 4 pages
http://dx.doi.org/10.1155/2013/397262
Research Article

The Near Subnormal Weighted Shift and Recursiveness

Group of DEFA, Department of Mathematics and Informatics, Faculté des Sciences, Université Moulay Ismail, BP 11201, Zitoune, Méknés, Morocco

Received 19 October 2012; Accepted 14 February 2013

Academic Editor: Chuanxi Qian

Copyright © 2013 R. Ben Taher and M. Rachidi. 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

We aim at studying the near subnormality of the unilateral weighted shifts, whose moment sequences are defined by linear recursive relations of finite order. Using the basic properties of recursive sequences, we provide a natural necessary condition, that ensure the near subnormality of this important class of weighted shifs. Some related new results are established; moreover, applications and consequences are presented; notably the notion of near subnormal completion weighted shift is implanted and explored.