Norm Retrievable Frames and Their Perturbation in Finite Dimensional Complex Hilbert Spaces |
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Authors: | M A Hasankhani Fard L Mohammadi Rad |
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Institution: | 1. Department of Mathematics, Vali-e-Asr University, Rafsanjan, Iranm.hasankhani@vru.ac.ir;3. Department of Mathematics, Vali-e-Asr University, Rafsanjan, Iran |
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Abstract: | In this article, we study the property of norm retrievability of spanning vectors in a finite dimensional complex Hilbert space ?. Using the set of zero trace operators on ? and two sets of self-adjoint operators on ? denoted by 𝒮1,0 and 𝒮1,1, we present some equivalent conditions to the norm retrievable frames in ?. We will also show that the property of norm retrievability for n-dimensional complex Hilbert space ? with n≠2 is stable under enough small perturbation of the frame set only for phase retrievable frames. |
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Keywords: | Frame norm retrievable frame phase retrievable frame |
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