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Description
This study examines the lower and upper bounds of the numerical radius and the Crawford number functions of bounded linear operators on Banach spaces. It also explores some convergence properties of these functions for sequences of uniformly converging Banach space operators. Later on, similar problems are addressed in the case of sectorial operators.
Keywords: Numerical radius, Crawford number, Sectorial operator
Open Problem: Determining the numerical radii of Banach space with constant operator coefficients of abstract linear functional delay differential-operator equations plays a crucial role in establishing asymptotic stability of these equations on the infinitive interval in the Theory of Boundary Value Problems.
References
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