Norm Retrievable Frames and Their Perturbation in Finite Dimensional Complex Hilbert Spaces

• Published in: Numerical functional analysis and optimization Vol. 38; no. 1; pp. 51 - 57
• Main Authors: Fard, M. A. Hasankhani, Rad, L. Mohammadi
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02-01-2017; Taylor & Francis Ltd
• Subjects: Equivalence; Frame; Frames; Hilbert space; Mathematical analysis; norm retrievable frame; Norms; Operators; Operators (mathematics); Optimization; Perturbation; Perturbation methods; phase retrievable frame; Quantum theory
• ISSN: 0163-0563; 1532-2467
• DOI: 10.1080/01630563.2016.1232733

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
1,0
and
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.