Operators and POVMs generated by Parseval frames
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908770521579520 |
|---|---|
| author | Kużel, Sergiusz Łukasiewicz, Piotr |
| author_facet | Kużel, Sergiusz Łukasiewicz, Piotr |
| contents | 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 $H_{E,e}$ and a positive operator-valued measure (POVM) $F_{E,e}$. This paper investigates in detail the relationship between the operator $H_{E, e}$ and the POVM $F_{E,e}$. Our results extend the classical correspondence between a self-adjoint operator generated by an orthonormal basis and its associated projection-valued (spectral) measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11225 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Operators and POVMs generated by Parseval frames Kużel, Sergiusz Łukasiewicz, Piotr Functional Analysis Mathematical Physics 46N50, 47N50, 46B15, 42C15 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 $H_{E,e}$ and a positive operator-valued measure (POVM) $F_{E,e}$. This paper investigates in detail the relationship between the operator $H_{E, e}$ and the POVM $F_{E,e}$. Our results extend the classical correspondence between a self-adjoint operator generated by an orthonormal basis and its associated projection-valued (spectral) measure. |
| title | Operators and POVMs generated by Parseval frames |
| topic | Functional Analysis Mathematical Physics 46N50, 47N50, 46B15, 42C15 |
| url | https://arxiv.org/abs/2601.11225 |