The Multiplicative Kowalski-Slodkowski Theorem for Hermitian Algebras
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915482695630848 |
|---|---|
| author | Brits, Rudi Hassen, Muhammad Toure, Cheick |
| author_facet | Brits, Rudi Hassen, Muhammad Toure, Cheick |
| contents | We prove, for Hermitian algebras, the multiplicative version of the Kowalski-Słodkowski Theorem which identifies the characters among the collection of all complex valued functions on a Banach algebra $A$ in terms of a spectral condition. Specifically, we show that, if $A$ is a Hermitian algebra, and if $ϕ:A\mapsto\mathbb C$ is a continuous function satisfying $ϕ(x)ϕ(y) \in σ(xy)$ for all $x,y\in A$ (where $σ$ denotes the spectrum), then either $ϕ$ or $-ϕ$ is a character of $A$; of course the converse holds as well. Our proof depends fundamentally on the existence of positive elements and square roots in these algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03663 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Multiplicative Kowalski-Slodkowski Theorem for Hermitian Algebras Brits, Rudi Hassen, Muhammad Toure, Cheick Functional Analysis 46H05, 46H15, 47A10 We prove, for Hermitian algebras, the multiplicative version of the Kowalski-Słodkowski Theorem which identifies the characters among the collection of all complex valued functions on a Banach algebra $A$ in terms of a spectral condition. Specifically, we show that, if $A$ is a Hermitian algebra, and if $ϕ:A\mapsto\mathbb C$ is a continuous function satisfying $ϕ(x)ϕ(y) \in σ(xy)$ for all $x,y\in A$ (where $σ$ denotes the spectrum), then either $ϕ$ or $-ϕ$ is a character of $A$; of course the converse holds as well. Our proof depends fundamentally on the existence of positive elements and square roots in these algebras. |
| title | The Multiplicative Kowalski-Slodkowski Theorem for Hermitian Algebras |
| topic | Functional Analysis 46H05, 46H15, 47A10 |
| url | https://arxiv.org/abs/2509.03663 |