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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 298982, 11 pages
http://dx.doi.org/10.1155/2013/298982
Research Article

New Characterizations of Riesz-Type Frames and Stability of Alternate Duals of Continuous Frames

School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

Received 11 April 2013; Accepted 21 May 2013

Academic Editor: Remi Leandre

Copyright © 2013 Zhong-Qi Xiang. 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 give new characterizations of Riesz-type frames, on equivalent conditions for a continuous frame to be a Riesz-type frame and on equivalency relations between Riesz-type frames and continuous frames. We characterize also the Riesz-type frames by using a bounded linear operator . Finally, we study the stability of alternate duals of continuous frames and we prove that if two continuous frames are close to each other, then we can find alternate duals of them which are close to each other.