Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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G-frames as Sums of Some g-orthonormal Bases

  • Abdollahpour, Mohammad Reza (Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili) ;
  • Najati, Abbas (Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili)
  • Received : 2011.05.14
  • Accepted : 2011.09.28
  • Published : 2013.03.23
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Abstract

In this paper we show that a $g$-frame for a Hilbert space $\mathcal{H}$ can be written as a linear combination of two $g$-orthonormal bases for $\mathcal{H}$ if and only if it is a $g$-Riesz basis for $\mathcal{H}$. Also, we show that every $g$-frame for a Hilbert space $\mathcal{H}$ is a multiple of a sum of three $g$-orthonormal bases for $\mathcal{H}$.

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References

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