G-Frame Representation and Invertibility of G-Bessel Multipliers
Received:June 25, 2012  Revised:November 22, 2012
Key Words: g-frames   g-orthonormal basis   controlled g-frames   weighted g-frames   g-frame multipliers.  
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Author NameAffiliation
A. ABDOLLAHI Department of Mathematics, College of Sciences, Shiraz University, Shiraz 71454, Iran 
E. RAHIMI Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran 
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      In this paper we show that every g-frame for an infinite dimensional Hilbert space $\mathcal{H}$ can be written as a sum of three g-orthonormal bases for $\mathcal{H}$. Also, we prove that every g-frame can be represented as a linear combination of two g-orthonormal bases if and only if it is a g-Riesz basis. Further, we show each g-Bessel multiplier is a Bessel multiplier and investigate the inversion of g-frame multipliers. Finally, we introduce the concept of controlled g-frames and weighted g-frames and show that the sequence induced by each controlled g-frame (resp., weighted g-frame) is a controlled frame (resp., weighted frame).
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