## Journal of Applied Mathematics

### Equivalency Relations between Continuous g-Frames and Stability of Alternate Duals of Continuous g-Frames in Hilbert ${C}^{*}$-Modules

Zhong-Qi Xiang

#### Abstract

We introduce the modular continuous g-Riesz basis to improve one existing result for continuous g-Riesz basis in Hilbert ${C}^{*}$-modules, and then we study the equivalency relations between continuous g-frames in Hilbert ${C}^{*}$-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 ${C}^{*}$-modules.

#### Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 192732, 11 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394808148

Digital Object Identifier
doi:10.1155/2013/192732

Mathematical Reviews number (MathSciNet)
MR3108947

Zentralblatt MATH identifier
06950546

#### Citation

Xiang, Zhong-Qi. Equivalency Relations between Continuous g-Frames and Stability of Alternate Duals of Continuous g-Frames in Hilbert ${C}^{*}$ -Modules. J. Appl. Math. 2013 (2013), Article ID 192732, 11 pages. doi:10.1155/2013/192732. https://projecteuclid.org/euclid.jam/1394808148

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