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<p>In this paper, we investigate operator-valued frames (OPV-frames) for phase (norm) retrieval. Firstly, we give a sufficient and necessary condition for phase retrievable OPV-frames in real finite-dimensional Hilbert spaces. Some conditions which are equivalent to phase retrievable OPV-frames are also presented. Secondly, we obtain some equivalent conditions to the norm retrievable OPV-frame in real and complex finite-dimensional Hilbert spaces. Finally, we show that the property of phase retrievable for real Hilbert spaces is stable under small perturbation of an OPV-frame. It is also shown that the property of norm retrievability is stable under enough small perturbations of an OPV-frame only for phase retrievable OPV-frames.</p>

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Phase and norm retrievable operator valued frames

  • 期刊论文

  • 发表日期：

    2025年8月4日

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  • Dongwei Li,
  • Yuxiang Xu

摘要

In this paper, we investigate operator-valued frames (OPV-frames) for phase (norm) retrieval. Firstly, we give a sufficient and necessary condition for phase retrievable OPV-frames in real finite-dimensional Hilbert spaces. Some conditions which are equivalent to phase retrievable OPV-frames are also presented. Secondly, we obtain some equivalent conditions to the norm retrievable OPV-frame in real and complex finite-dimensional Hilbert spaces. Finally, we show that the property of phase retrievable for real Hilbert spaces is stable under small perturbation of an OPV-frame. It is also shown that the property of norm retrievability is stable under enough small perturbations of an OPV-frame only for phase retrievable OPV-frames.