Between the von Neumann inequality and the Crouzeix conjecture
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2019
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912355364896768 |
|---|---|
| author | Pagacz, Patryk Pietrzycki, Paweł Wojtylak, Michał |
| author_facet | Pagacz, Patryk Pietrzycki, Paweł Wojtylak, Michał |
| contents | A new concept of a deformed numerical range $W^ρ(T)$ is introduced. Here $T$ is a bounded linear operator or a matrix and $ ρ\in[1,+\infty)$ is a parameter. Each $W^ρ(T)$ is a closed convex set that contains the spectrum of $T$. Furthermore, $W^ρ(T)$ is decreasing with respect to $ ρ$ and $W^2(T)$ coincides with the numerical range. It is also shown that $W^ρ(T)$ is contained in the closed unit disc if and only if $T$ has a $ρ$ unitary dilation in the sense of Nágy-Foia\c s. The spectral constants of $W^ρ(T)$ are investigated, it is shown that it is monotone and continuous with respect to the parameter $ ρ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1907_06228 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Between the von Neumann inequality and the Crouzeix conjecture Pagacz, Patryk Pietrzycki, Paweł Wojtylak, Michał Functional Analysis A new concept of a deformed numerical range $W^ρ(T)$ is introduced. Here $T$ is a bounded linear operator or a matrix and $ ρ\in[1,+\infty)$ is a parameter. Each $W^ρ(T)$ is a closed convex set that contains the spectrum of $T$. Furthermore, $W^ρ(T)$ is decreasing with respect to $ ρ$ and $W^2(T)$ coincides with the numerical range. It is also shown that $W^ρ(T)$ is contained in the closed unit disc if and only if $T$ has a $ρ$ unitary dilation in the sense of Nágy-Foia\c s. The spectral constants of $W^ρ(T)$ are investigated, it is shown that it is monotone and continuous with respect to the parameter $ ρ$. |
| title | Between the von Neumann inequality and the Crouzeix conjecture |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/1907.06228 |