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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 192732, 11 pages
http://dx.doi.org/10.1155/2013/192732
Research Article

Equivalency Relations between Continuous g-Frames and Stability of Alternate Duals of Continuous g-Frames in Hilbert -Modules

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

Received 8 April 2013; Revised 6 August 2013; Accepted 16 August 2013

Academic Editor: Hak-Keung Lam

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 introduce the modular continuous g-Riesz basis to improve one existing result for continuous g-Riesz basis in Hilbert -modules, and then we study the equivalency relations between continuous g-frames in Hilbert -modules, and, in particular, we obtain two necessary and sufficient conditions under which two continuous g-frames are similar. Finally, we generalize a stability result for alternate duals of g-frames in Hilbert spaces to alternate duals of continuous g-frames in Hilbert -modules.