Norm retrieval and phase retrieval by projections

Abstract

We make a detailed study of norm retrieval. We give several classification theorems for norm retrieval and give a large number of examples to go with the theory. One consequence is a new result about Parseval frames: If a Parseval frame is divided into two subsets with spans W1, W2 and Wl ∩ W2 = {0}, then W1 ⊥ W2.