IJPAM: Volume 105, No. 4 (2015)

G-FRAMES IN HILBERT PRO-C*-MODULES

N. Haddadzadeh
Department of Mathematics
Abadan Branch
Islamic Azad University
Abadan, IRAN


Abstract. G-frames are generalized frames which include ordinary frames, bounded invertible linear operators, as well as many recent generalizations of frames, e.g., bounded quasi-projectors and frames of subspaces. G-frames are natural generalizations of frames which provide more choices on analyzing functions from frame expansion coefficients. First, they were defined in Hilbert spaces and then generalized on C*-Hilbert modules. In this paper, we first generalize the concept of g-frames to Hilbert modules over pro-C*-algebras. Then, we introduce the g-frame operators in such spaces and show that they share many useful properties with their corresponding notions in Hilbert spaces. We also show that, by having a g-frame and an invertible operator in this spaces, we can produce the corresponding dual g-frame. Finally we introduce the canonical dual g-frames and provide a reconstruction formula for the elements of such Hilbert modules.

Received: September 6, 2015

AMS Subject Classification:

Key Words and Phrases: pro-C*-algebra, Hilbert modules, G-frames, frame operators

Download paper from here.




DOI: 10.12732/ijpam.v105i4.13 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 105
Issue: 4
Pages: 727 - 743


Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).