Joint numerical radius of Tuples: Extreme points, subdifferential set and Gateaux derivative
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918085225611264 |
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| author | Mal, Arpita |
| author_facet | Mal, Arpita |
| contents | Suppose $\mathcal{Z}$ is the space of all tuples of operators on a finite-dimensional Banach space endowed with the joint numerical radius norm. We obtain the structure of the extreme points of the dual unit ball of $\mathcal{Z}.$ Using this, we derive an expression for the subdifferential set of the joint numerical radius of a tuple in $\mathcal{Z}.$ Applying this expression, we characterize smooth tuples and Birkhoff-James orthogonality in $\mathcal{Z}.$ Finally, we obtain the Gateaux derivative of the joint numerical radius of a tuple. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04700 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Joint numerical radius of Tuples: Extreme points, subdifferential set and Gateaux derivative Mal, Arpita Functional Analysis Suppose $\mathcal{Z}$ is the space of all tuples of operators on a finite-dimensional Banach space endowed with the joint numerical radius norm. We obtain the structure of the extreme points of the dual unit ball of $\mathcal{Z}.$ Using this, we derive an expression for the subdifferential set of the joint numerical radius of a tuple in $\mathcal{Z}.$ Applying this expression, we characterize smooth tuples and Birkhoff-James orthogonality in $\mathcal{Z}.$ Finally, we obtain the Gateaux derivative of the joint numerical radius of a tuple. |
| title | Joint numerical radius of Tuples: Extreme points, subdifferential set and Gateaux derivative |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2507.04700 |