| 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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| Abstract: |
| 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). |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2013.04.002 |
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