Norm Retrievable Frames and Their Perturbation in Finite Dimensional Complex Hilbert Spaces. (2nd January 2017)

• Record Type: Journal Article
• Authors: Fard, M. A. Hasankhani; Rad, L. Mohammadi
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 1(2017)
• Page Start: 51
• Page End: 57
• Publication Date: 2017-01-02
• Subjects: Frame -- norm retrievable frame -- phase retrievable frame; 32C15 -- 42C15; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1232733
• Languages: English
• ISSNs: 0163-0563

Abstract

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.