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
投稿时间:2012-06-25  最后修改时间:2012-11-22
DOI:10.3770/j.issn:2095-2651.2013.04.002
中文关键词:  g-frames  g-orthonormal basis  controlled g-frames  weighted g-frames  g-frame multipliers.
英文关键词:g-frames  g-orthonormal basis  controlled g-frames  weighted g-frames  g-frame multipliers.
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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 
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中文摘要:
      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).
英文摘要:
      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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