A. ABDOLLAHI,E. RAHIMI.G-Frame Representation and Invertibility of G-Bessel Multipliers[J].数学研究及应用,2013,33(4):392~402
G-Frame Representation and Invertibility of G-Bessel Multipliers
G-Frame Representation and Invertibility of G-Bessel Multipliers

DOI：10.3770/j.issn:2095-2651.2013.04.002

 作者 单位 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

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).

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).