Joint numerical radius of Tuples: Extreme points, subdifferential set and Gateaux derivative
Abstract
Suppose 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 Z. Using this, we derive an expression for the subdifferential set of the joint numerical radius of a tuple in Z. Applying this expression, we characterize smooth tuples and Birkhoff-James orthogonality in Z. Finally, we obtain the Gateaux derivative of the joint numerical radius of a tuple.
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