Tight and random nonorthogonal fusion frames

Abstract

Abstract. This paper continues the investigation of nonorthogonal fusion frames started in [7]. First we show that tight nonorthogonal fusion frames a relatively easy to com by. In order to do this we need to establish a classification of how to to wire a self adjoint operator as a product of (nonorthogonal) projection operators. We also discuss the link between nonorthogonal fusion frames and positive operator valued measures, we define and study a nonorthogonal fusion frame potential, and we introduce the idea of random nonorthogonal fusion frames.

Local-to-global frames and applications to dynamical sampling problem

“…For the next proposition, we recall the definition of fusion frames (see [17,18,19,31] and the references therein) and completeness for a system of orthogonal projectors. Definition 2.2.…”

On symmetric decompositions of positive operators

“…The idea, originating in [9, Corollary 5.2], is that among N subspaces of fixed dimension in C d , there must be at least a pair with "small" principal angles. This result has been generalized to subspaces with weights in [2,Theorem 3.4], and then to arbitrary positive semidefinite operators with fixed trace in [4,Proposition 4.1]. In the result below, we slightly generalize this last result, by removing the fixed trace condition.…”