The Hyperrigidity Conjecture for compact convex sets in $\mathbb{R}^2$
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915024668196864 |
|---|---|
| author | Scherer, Marcel |
| author_facet | Scherer, Marcel |
| contents | We prove that for every compact, convex subset $K\subset\mathbb{R}^2$ the operator system $A(K)$, consisting of all continuous affine functions on $K$, is hyperrigid in the C*-algebra $C(\mathrm{ex}(K))$. In particular, this result implies that the weak and strong operator topologies coincide on the set $$
\{ T\in\mathcal{B}(H);\ T\ \mathrm{normal}\ \mathrm{and}\ σ(T)\subset \mathrm{ex}(K) \}.
$$ Our approach relies on geometric properties of $K$ and generalizes previous results by Brown. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11709 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Hyperrigidity Conjecture for compact convex sets in $\mathbb{R}^2$ Scherer, Marcel Functional Analysis Primary 46L05, 46L07, 47B15 We prove that for every compact, convex subset $K\subset\mathbb{R}^2$ the operator system $A(K)$, consisting of all continuous affine functions on $K$, is hyperrigid in the C*-algebra $C(\mathrm{ex}(K))$. In particular, this result implies that the weak and strong operator topologies coincide on the set $$ \{ T\in\mathcal{B}(H);\ T\ \mathrm{normal}\ \mathrm{and}\ σ(T)\subset \mathrm{ex}(K) \}. $$ Our approach relies on geometric properties of $K$ and generalizes previous results by Brown. |
| title | The Hyperrigidity Conjecture for compact convex sets in $\mathbb{R}^2$ |
| topic | Functional Analysis Primary 46L05, 46L07, 47B15 |
| url | https://arxiv.org/abs/2411.11709 |