Operators and POVMs generated by Parseval frames
Abstract
Let F be a Parseval frame in a Hilbert space and let E be a set of real numbers. From these data, we construct an operator HE,e and a positive operator-valued measure (POVM) FE,e. This paper investigates in detail the relationship between the operator HE, e and the POVM FE,e. Our results extend the classical correspondence between a self-adjoint operator generated by an orthonormal basis and its associated projection-valued (spectral) measure.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.