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arXiv · 2507.04700

Joint numerical radius of Tuples: Extreme points, subdifferential set and Gateaux derivative

Arpita Mal
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Abstract

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.

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Arpita Mal. 2025-07-07. Joint numerical radius of Tuples: Extreme points, subdifferential set and Gateaux derivative. https://arxiv.org/abs/2507.04700

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