Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.02042 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912410780041216 |
|---|---|
| author | Alakhrass, Mohammad |
| author_facet | Alakhrass, Mohammad |
| contents | In this paper, we investigate the generalized numerical radius $ω_N$, associated with a matrix norm $N$ defined by $ω_N(X) = \sup_{θ\in \mathbb{R}} N(\operatorname{Re}(e^{iθ}X))$. We focus on matrices whose numerical ranges are contained in sectors of the complex plane (sectorial matrices) and derive upper bounds for $ω_N(XY)$ and $ω_N(X \circ Y)$ for such matrices $X$ and $Y$. Our results generalize and refine well known numerical radius inequalities. Several known inequalities for $ω(X)$ are recovered as special cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02042 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | General Numerical Radius for Products of Sectorial Matrices Alakhrass, Mohammad Functional Analysis In this paper, we investigate the generalized numerical radius $ω_N$, associated with a matrix norm $N$ defined by $ω_N(X) = \sup_{θ\in \mathbb{R}} N(\operatorname{Re}(e^{iθ}X))$. We focus on matrices whose numerical ranges are contained in sectors of the complex plane (sectorial matrices) and derive upper bounds for $ω_N(XY)$ and $ω_N(X \circ Y)$ for such matrices $X$ and $Y$. Our results generalize and refine well known numerical radius inequalities. Several known inequalities for $ω(X)$ are recovered as special cases. |
| title | General Numerical Radius for Products of Sectorial Matrices |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2506.02042 |