Weighted $\delta$-numerical radius and weighted $\delta$-Crawford number functions

Abstract

In this study, we investigate several important algebraic and smoothness properties of the weighted $\delta$-numerical radius and the weighted $\delta$-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.

Keywords

• weighted $\delta$-numerical radius
• weighted $\delta$-Crawford number
• sectorial operator

Supporting Institution

There is no supporting institution for this work.

Ethical Statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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