Norm Retrievable Frames and Their Perturbation in Finite Dimensional Complex Hilbert Spaces. (2nd January 2017) - Fard, M. A. Hasankhani; Rad, L. Mohammadi
ABSTRACT: In this article, we study the property of norm retrievability of spanning vectors in a finite dimensional complex Hilbert space ℋ . Using the set of zero trace operators on ℋ and two sets of self-adjoint operators on ℋ denoted by 𝒮 1, 0 and 𝒮 1, 1, we present some equivalent conditions to the norm retrievable frames in ℋ . We will also show that the property of norm retrievability for n -dimensional complex Hilbert space ℋ with n ≠2 is stable under enough small perturbation of the frame set only for phase retrievable frames.