Tight and random nonorthogonal fusion frames

TL;DR

This paper explores the construction and properties of tight nonorthogonal fusion frames, including their classification, connection to positive operator valued measures, and the introduction of random nonorthogonal fusion frames.

Contribution

It provides a classification method for wiring self-adjoint operators as products of nonorthogonal projections and introduces the concept of random nonorthogonal fusion frames.

Findings

Tight nonorthogonal fusion frames are relatively easy to construct.

A classification of self-adjoint operators as products of nonorthogonal projections is established.

The link between nonorthogonal fusion frames and positive operator valued measures is analyzed.

Abstract

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.