Weighted δ-Numerical Radius and Weighted δ-Crawford Number Functions

In this study, we investigate several important algebraic and smoothness properties of the weighted δ-numerical radius and the weighted δ-Crawford number functions. We also derive estimates of the upper and lower bounds of these weighted functions. Particular attention is paid to the sectorial case of the operators under consideration. The results obtained not only extend certain known results in the literature but also provide a variety of useful techniques that may contribute to further developments in this field.